IA Scholar Query: Resolving finite indeterminacy: A definitive constructive universal prime ideal theorem.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 30 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440F–J
https://scholar.archive.org/work/cn4pwk4efnaa3ba27vpt6ux6ca
Fabergé, Peter Carl (1846Carl ( -1920)) . Russian jeweller, of French descent. He achieved fame by the ingenuity and extravagance of the jewelled objects (especially Easter eggs) he devised for the Russian nobility and the tsar in an age of ostentatious extravagance which ended on the outbreak of World War I. He died in Switzerland.work_cn4pwk4efnaa3ba27vpt6ux6caWed, 30 Nov 2022 00:00:00 GMTThe algebraic dynamics of the pentagram map
https://scholar.archive.org/work/wpg2nhsanzbshf5efsektxkz4a
The pentagram map, introduced by Schwartz [The pentagram map. Exp. Math.1(1) (1992), 71–81], is a dynamical system on the moduli space of polygons in the projective plane. Its real and complex dynamics have been explored in detail. We study the pentagram map over an arbitrary algebraically closed field of characteristic not equal to 2. We prove that the pentagram map on twisted polygons is a discrete integrable system, in the sense of algebraic complete integrability: the pentagram map is birational to a self-map of a family of abelian varieties. This generalizes Soloviev's proof of complex integrability [F. Soloviev. Integrability of the pentagram map. Duke Math. J.162(15) (2013), 2815–2853]. In the course of the proof, we construct the moduli space of twisted n-gons, derive formulas for the pentagram map, and calculate the Lax representation by characteristic-independent methods.MAX H. WEINREICHwork_wpg2nhsanzbshf5efsektxkz4aFri, 25 Nov 2022 00:00:00 GMTOn the threefold minimal model program in positive and mixed characteristic
https://scholar.archive.org/work/adungoz2tnew5o72qungiyum6u
This dissertation explores the Minimal Model Program (MMP) in positive and mixed characteristic in dimension three with a particular focus on outputs of the program. In purely positive characteristic we combine the program with a detailed study of conic bundles to prove a birational boundedness result. We show that given a suitable set of log Calabi-Yau varieties, we can construct a bounded family containing bres birational to any member of the chosen set. For threefolds over a base of dimension at least one, we resolve the Abundance Conjecture for klt pairs in joint work with F. Bernasconi and I. Brivio. Showing in particular that every klt minimal model in mixed characteristic admits an Iitaka Fibration. This is then applied to prove an Invariance of Plurigenera result for suitable families of surfaces. Finally we consider outstanding questions around Mori brations in mixed characteristic. We show that every klt threefold MMP terminates and that any two Mori bre space outputs of an MMP from the same starting pair are connected by a series of Sarkisov links. As part of this we prove a mixed characteristic Finiteness of Minimal Models result. While the proof is focused in dimension three, the arguments work in any generality given that the requisite MMP results are known.Liam Stigant, Paolo Cascini, Engineering And Physical Sciences Research Council (EPSRC)work_adungoz2tnew5o72qungiyum6uTue, 15 Nov 2022 00:00:00 GMTAlgebraic characterizations of homeomorphisms between algebraic varieties
https://scholar.archive.org/work/fk45kphbkrejxihrqmeuenqzbq
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology and for a strong topology that we introduce. Our answers involve a study of seminormalization and saturation for morphisms between algebraic varieties, together with an interpretation in terms of continuous rational functions on the closed points of an algebraic variety. The continuity refers to the strong topology which is the usual Euclidean topology in the complex case, whereas it comes from the theory of real closed fields otherwise.François Bernard, Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarezwork_fk45kphbkrejxihrqmeuenqzbqTue, 15 Nov 2022 00:00:00 GMTQuasi-projective varieties with orbifold fundamental groups
https://scholar.archive.org/work/7ctauzwc3vcxhbqpahlpkcuxsi
In this work we study smooth complex quasi-projective varieties whose fundamental group is a free product of cyclic groups. In particular, we prove the existence of a (maybe irrational) pencil from the quasi-projective variety to a Riemann surface (endowed with an orbifold structure) which induces an isomorphism of (orbifold) fundamental groups. The orbifold structure is given by the multiple fibers of the pencil. Associated with this result, we prove addition-deletion Lemmas of fibers in the pencil which explain how these operations affect the fundamental group of the quasi-projective variety. Our methods also allow us to produce curves whose fundamental group of their complement is a free product of cyclic groups, generalizing classical results on C_p,q curves and torus type projective sextics, and showing how general this phenomenon is.José Ignacio Cogolludo-Agustín, Eva Elduquework_7ctauzwc3vcxhbqpahlpkcuxsiMon, 31 Oct 2022 00:00:00 GMTQuantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
https://scholar.archive.org/work/kwil4dkbkjhfrpgkpcrhgtmwta
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer's records. However, our "let quantum be quantum" approach poses questions absent in Bohr's Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply "too relative", and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born's rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the 'quantum theory of the classical' one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born's rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.Wojciech Hubert Zurekwork_kwil4dkbkjhfrpgkpcrhgtmwtaMon, 24 Oct 2022 00:00:00 GMTSpherical cosmological models: an alternative cosmology
https://scholar.archive.org/work/f3mdfrttjvc2rkxkw4ew2o6kea
The properties of universes are explored that are entirely in the interior of black holes in another universe, a 'mother universe'. It is argued that these models offer a paradigm that may shed a new light on old cosmological problems. The geometry of such a universe is discussed including how it would appear to the observer. The Hubble parameter is direction dependent, but it is argued that the interpretation of any such dependence will be hard to separate from local inhomogeneities. The models do not originate from a big bang, but rather from an initial collapse and subsequent infall, that started probably a very long time ago, presumably much earlier than the accepted age of the universe. The relation to the concordance model is discussed and it is shown that a lot of the existing theory can be taken over into the proposed models. The universe has an edge, which is an ordinary spherical surface in 3 dimensions. That sphere acts as a gravitational mirror as seen from inside the universe, but it does not mirror redshift. The same object can thus be seen in direct sight and in reflection, although with different redshifts, different ages and different aspect angles. The models do not need dark energy, but they need dark matter, of course. Since the models are closed and neutrino's are nowadays believed to have mass, neutrino's can be reconsidered as candidates for the dark matter. As a bonus result from this paradigm, mass ejection from black holes is shown to be possible, which links that process to the controversial anomalous galaxy redshifts. Finally, we show that gravitational mass and inertial mass are proportional, and that the inertial acceleration scales as c^2/M, with M a characteristic length scale of the universe.Herwig Dejonghework_f3mdfrttjvc2rkxkw4ew2o6keaThu, 13 Oct 2022 00:00:00 GMTHeight moduli on cyclotomic stacks and counting elliptic curves over function fields
https://scholar.archive.org/work/qqop7ivu6zap3augww5oeb3kem
For proper stacks, unlike schemes, there is a distinction between rational and integral points; we show that this distinction exactly accounts for the main term and lower order terms appearing in counts of elliptic curves over function fields. More generally, using the theory of twisted stable maps and the stacky height functions recently introduced by Ellenberg, Zureick-Brown, and the third author, we construct finite type moduli spaces which parametrize rational points of fixed height on a large class of stacks, so-called cyclotomic stacks. As a by product, we obtain the Northcott property as well as a generalization of Tate's algorithm for cyclotomic stacks, and propose an answer to a question of Venkatesh.Dori Bejleri, Jun-Yong Park, Matthew Satrianowork_qqop7ivu6zap3augww5oeb3kemMon, 10 Oct 2022 00:00:00 GMTCurve classes on conic bundle threefolds and applications to rationality
https://scholar.archive.org/work/ksbobx524nac5f3arkqhrywerm
We undertake a study of conic bundle threefolds π X→ W over geometrically rational surfaces whose associated discriminant covers Δ̃→Δ⊂ W are smooth and geometrically irreducible. First, we determine the structure of the group CH^2 X_k of rational equivalence classes of curves. Precisely, we construct a Galois-equivariant group homomorphism from CH^2X_k to a group scheme associated to the discriminant cover Δ̃→Δ of X. The target group scheme is a generalization of the Prym variety of Δ̃→Δ and so our result can be viewed as a generalization of Beauville's result that the algebraically trivial curve classes on X_k are parametrized by the Prym variety. Next, we use our structural result on curve classes to study rationality obstructions, in particular the refined intermediate Jacobian torsor (IJT) obstruction recently introduced by Hassett–Tschinkel and Benoist–Wittenberg. We show that for conic bundle threefolds there is no strongest (known) rationality obstruction. Precisely, we construct a geometrically rational irrational conic bundle threefold where the IJT obstruction cannot witness irrationality (irrationality is detected through the real topology) and a geometrically rational irrational conic bundle threefold where all classical rationality obstructions vanish and the IJT obstruction is needed to prove irrationality.Sarah Frei, Lena Ji, Soumya Sankar, Bianca Viray, Isabel Vogtwork_ksbobx524nac5f3arkqhrywermTue, 20 Sep 2022 00:00:00 GMTSmall resolutions of special three-dimensional varieties
https://scholar.archive.org/work/xhvwn2dszbb4hf2tnezq3frq4u
This is an English translation of Werner's 1987 dissertation "Kleine Aufl\"osungen spezieller dreidimensionaler Variet\"aten," originally published as Bonner Mathematische Schriften No. 186.Jürgen Werner, Simon Venter, Nicolas Addingtonwork_xhvwn2dszbb4hf2tnezq3frq4uTue, 13 Sep 2022 00:00:00 GMTSteenrod operations and algebraic classes
https://scholar.archive.org/work/n4wat6jknnbhjcrldlpmmdf22a
Based on a relative Wu theorem in étale cohomology, we study the compatibility of Steenrod operations on Chow groups and on étale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic cohomology classes over various fields (ℂ, ℝ, 𝔽_p, 𝔽_q). We also use Steenrod operations to study the mod 2 cohomology classes of a compact 𝒞^∞ manifold M that are algebraizable, i.e. algebraic on some real algebraic model of M. We give new examples of algebraizable and non-algebraizable classes, answering questions of Benedetti, Dedò and Kucharz.Olivier Benoistwork_n4wat6jknnbhjcrldlpmmdf22aThu, 08 Sep 2022 00:00:00 GMTModuli of genus one curves with two marked points as a weighted blow-up
https://scholar.archive.org/work/rokmxxmxuvazxh3557w2tiobnq
We give an explicit description of ℳ_1,2 as a weighted blow-up of a weighted projective stack. We use this description to compute the Brauer group of ℳ_1,2;S over any base scheme S where 6 is invertible, and the integral Chow rings of ℳ_1,2 and ℳ_1,2.Giovanni Inchiostrowork_rokmxxmxuvazxh3557w2tiobnqThu, 25 Aug 2022 00:00:00 GMTLIPIcs, Volume 240, COSIT 2022, Complete Volume
https://scholar.archive.org/work/7m7bfxazsra63myunecp6u6qgm
LIPIcs, Volume 240, COSIT 2022, Complete VolumeToru Ishikawa, Sara Irina Fabrikant, Stephan Winterwork_7m7bfxazsra63myunecp6u6qgmMon, 22 Aug 2022 00:00:00 GMTQuantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
https://scholar.archive.org/work/cpiljzdtnvfpdprc5oh27qlnpm
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that -- when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate) -- these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate.Wojciech Hubert Zurekwork_cpiljzdtnvfpdprc5oh27qlnpmThu, 18 Aug 2022 00:00:00 GMTClassifying spaces of finite groups of tame representation type
https://scholar.archive.org/work/nkf4gyhojjbhroux7ytbz55d6u
Thanks to the work of Karin Erdmann, we know a great deal about the representation theory of blocks of finite groups with tame representation type. Our purpose here is to examine the p-completed classifying spaces of these blocks and their loop spaces. We pay special attention to the A_∞ algebra structures, and singularity and cosingularity categories.David J. Bensonwork_nkf4gyhojjbhroux7ytbz55d6uTue, 16 Aug 2022 00:00:00 GMTThe Authorization and Glorification of Plunder
https://scholar.archive.org/work/j65qh4whure4dac3gd4pv2uhru
Research in taxation often treats it as a branch of law or economics, but in this thesis I argue that this obscures the fact that tax systems are not based on scientific, techno-rational principles, but are socially constructed phenomena, embodying fundamental, value-based decisions imbricated in power relationships. I demonstrate that throughout history tax systems have reflected the prevailing state form and the dominant power relationships underpinning them and that we are currently living in a neoliberal state, in which societal relations are determined by economic principles. I therefore argue that the UK tax system tends to be utilized to encourage individuals to engage in economic, entrepreneurial activity and are presented as being governed by techno-rational, economic principles, but are, in fact, a rationalizing discourse for the transfer of power from labour to capital and from poorer to wealthier taxpayers. This transformation is underpinned by the exercise of power, but in a neoliberal state power operates in a covert, capillary fashion through assemblages and the construction of knowledge, rather than in an overt, hierarchical fashion. I demonstrate how the contemporary debates relating to tax simplification and the use of general principles rather than detailed rules in tax legislation have been, or might be, used to further entrench neoliberal values in the tax system, but that the failure to achieve significant simplification due to its open and transparent nature demonstrates the limits of power and the more opaque nature of general principles might have more potential for achieving this. However, no power can be absolute and I argue that the increased public interest in and awareness of taxation since 2010, which led to the emergence of UK Uncut, demonstrates that there is always the potential for resistance to a hegemonic discourse, which may lead to the emergence of alternative discourses.Malcolm Jameswork_j65qh4whure4dac3gd4pv2uhruThu, 04 Aug 2022 00:00:00 GMTEquivariant Degenerations of Plane Curve Orbits
https://scholar.archive.org/work/yseax4w3uffoxolu4mirrs4zam
In a series of papers, Aluffi and Faber computed the degree of the GL_3 orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how orbits degenerate under some natural specializations, yielding a fairly complete picture in the case of plane quartics.Mitchell Lee, Anand Patel, Dennis Tsengwork_yseax4w3uffoxolu4mirrs4zamSun, 31 Jul 2022 00:00:00 GMTZMK Zeitschrift für Medien- und Kulturforschung. Focus Producing Places
https://scholar.archive.org/work/k6pikcnpifgrhnvaz7iluioftu
and object-but, as a consequence, also the distinction of object and operation becomes a relative and transient one, very much like the one between place and space, place and non-place. It is quite clear that these two types of place-generating operations are interrelated in their turn. The operation of differentiation is not possible without decoupling of the formerly coherent and without a certain momentum of touch and tactility, as the operation of coupling requires distinct entities or operations, which are subject to the operation of coupling. The example of recent positioning and navigation technologies illustrates the interrelation of the two types very clearly. The question remains, though, as to how we could ascribe a place to such entities and operations, which do not interrelate, positively or negatively, and which do not touch each other, cross each other, affect each other, or attach to each other. Are there places that are being produced not via coupling, be it firm or loose, nor via distinction of identity and difference, but via an otherness, which doesn't even allow for comparison nor for contact? Are there places of and for objects and operations that do not share anything with other entities, which are unable to inhabit the same place? And, if so, would such a place still fall under the concept of producing places in the double meaning mentioned initially? Wouldn't it rather, instead of being productive, have no impact and no effect whatsoever, and wouldn't it insofar figure as a mere and pure place residing in itself, a sheer place of being? And if so, wouldn't we have to concede that such a place cannot be produced, but just arrive? The question is very relevant philosophically, but it is also of notable practical relevance as far as media cultures and places of media and in media are concerned. Different media, serving as tools of distinction and coupling, produce different places in diverse manners-but do they cooperate in placing operations, do they share places at all, do they even have places? In McLuhan, we find the metaphor of two galaxies (i.e. media cultures and media universes) crossing each other on their way through outer space without interference, without touching, without even contacting or affecting each other in the slightest way. Does this take place? Do they, and does their non-encounter, inhabit one place at all? How could we conceive of such a place? Do non-interference and disentanglement, and do refraining and abstaining from productivity and operativity have a sitting room?(:Unkn) Unknown, Mediarep.Org, Lorenz Engell, Bernhard Siegertwork_k6pikcnpifgrhnvaz7iluioftuTue, 21 Jun 2022 00:00:00 GMTFoundations for Meaning and Understanding in Human-centric AI
https://scholar.archive.org/work/joonfnadkrf2pab5rsubz2f7sq
MUHAI is a European consortium funded by the EU Pathfinder program that studies how it is possible to build AI systems that rest on meaning and understanding. We call this kind of AI meaningful AI in contrast to AI that rests exclusively on the use of statistically acquired pattern recognition and pattern completion. Because meaning and understanding are rather vague and overloaded notions there is no obvious research path to achieve it. The consortium has therefore set up a task early on in the project to explore how understanding is being discussed and treated in other human-centred research fields, more specifically in social brain science, social psychology, linguistics, semiotics, economics, social history and medicine. Our explorations have yielded a wealth of insights: about understanding in general and the role of narratives in this process, about possible applications of meaningful AI in a diverse set of human-centred fields, and about the technology gaps that need to be plugged to achieve meaningful AI. This volume summarizes the outcome of these consultations. It has three main parts: I. A general introduction, II. A series of chapters reporting on what understanding means in various human-centered research fields other than AI, and III. A short conclusion identifying key research topics for meaning-based human-centric AI.Steels, Luc (ed.)work_joonfnadkrf2pab5rsubz2f7sqSun, 19 Jun 2022 00:00:00 GMTStatic Analysis of Probabilistic Programs: An Algebraic Approach
https://scholar.archive.org/work/zlv4j3kxgndxrcvg7g3ukozhbu
Probabilistic programs are programs that can draw random samples from probability distributions and involve random control flows. They are becoming increasingly popular and have been applied in many areas such as algorithm design, cryptographic protocols, uncertainty modeling, and statistical inference. Formal reasoning about probabilistic programs comes with unique challenges, because it is usually not tractable to obtain the exact result distributions of probabilistic programs. This thesis focuses on an algebraic approach for static analysis of probabilistic programs. The thesis first provides a brief background on measure theory and introduces an imperative arithmetic probabilistic programming language Appl with a novel hyper-graph program model. Second, the thesis presents an algebraic denotational semantics for Appl that can be instantiated with different models of nondeterminism. The thesis also develops a new model of nondeterminism that involves nondeterminacy among state transformers and presents a domain-theoretic characterization of the new model. Based on the algebraic denotational semantics, the thesis proposes a general algebraic framework PMAF for designing, implementing, and proving the correctness of static analyses of probabilistic programs. The thesis also includes a concrete static analysis—central-moment analysis for cost accumulators in probabilistic programs—and elaborates implementation strategies to improve the usability and efficiency of the analysis. There is a gap between the general PMAF framework and the central-moment analysis, in the sense that the former is based on abstraction and iterative approximation, but the latter is based on constraint solving. The thesis provides some preliminary results on bridging the gap, via the development of novel regular hyper-path expressions, which finitely represent possibly-infinite hyperpaths on control-flow hyper-graphs of probabilistic programs without nondeterminism, and DMKAT algebraic structures, which can be used to interpret regular hyp [...]Di Wangwork_zlv4j3kxgndxrcvg7g3ukozhbuMon, 06 Jun 2022 00:00:00 GMT