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Arc lifting for the Nash manifold [article]

John Atwell Moody
2020 arXiv   pre-print
In addition a theorem about valuations is proven.  ...  A theorem of Functorial Affinization of Nash's manifold is proven here giving necessary and sufficient conditions to lift a holomorphic arc to the smooth locus of the Nash manifold.  ...  A coherent sheaf D on a quasiprojective scheme is 'coprimary' (generalizing the definition given in Algebre Local, Multiplicities' [20] ) if there is a prime ideal sheaf P so that if there is any prime  ... 
arXiv:1103.5723v10 fatcat:amrlgr3q4bfsfa6xj3gcih5xrm

Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta-functions, notes on the work of Shinichi Mochizuki

Ivan Fesenko
2015 European Journal of Mathematics  
In a series of preprints released several years ago, Mochizuki introduced a vast collection of new ideas and methods related to arithmetic deformation.  ...  Abstract These notes survey the main ideas, concepts and objects of the work by Shinichi Mochizuki on inter-universal Teichmüller theory (Inter-universal Teichmüller theory I-IV, 2012-2015) which might  ...  Work on this text was partially supported by University of Nottingham and EPSRC programme grant EP/M024830.  ... 
doi:10.1007/s40879-015-0066-0 fatcat:xrpw4vw74jd5ved7srzh3jnksy

Arithmetic dynamics on smooth cubic surfaces [article]

Solomon Vishkautsan
2014 arXiv   pre-print
We present results describing the sets of K and K̅-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity.  ...  Finally, we give a dynamical result relating to the Mordell--Weil problem on cubic surfaces.  ...  the maximal ideal in O p . • κ p is the residue field of the prime p (i.e.  ... 
arXiv:1307.3205v2 fatcat:mnrlapvnvza2vjxrfmtya32p5a

Newton-Okounkov bodies and Segre classes [article]

Paolo Aluffi
2018 arXiv   pre-print
Given a homogeneous ideal in a polynomial ring over C, we adapt the construction of Newton-Okounkov bodies to obtain a convex subset of Euclidean space such that a suitable integral over this set computes  ...  the Segre zeta function of the ideal.  ...  The indeterminacies of ϕ s are resolved by the closure Γ s of the graph of ϕ s , a subvariety of dimension n of P n × P Ns .  ... 
arXiv:1809.07344v1 fatcat:v453zp4ci5dyvbphqil2g6r2rm

The jumping coefficients of non-Q-Gorenstein multiplier ideals

Patrick Graf
2016 Journal of Algebra  
We also obtain that outside of W, the multiplier ideal reduces to the test ideal modulo sufficiently large primes p ≫ 0.  ...  Let a ⊂ O_X be a coherent ideal sheaf on a normal complex variety X, and let c > 0 be a real number.  ...  Furthermore, it answers a question of Rossi [Ros68, p. 72] asking for a universal property of his construction. Definition 6.1 (Resolution of a sheaf) .  ... 
doi:10.1016/j.jalgebra.2015.11.024 fatcat:ssisajbozvc4tpr2x43ol2xhyi

Indeterministic finite-precision physics and intuitionistic mathematics [article]

Tein van der Lugt
2021 arXiv   pre-print
Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see,  ...  Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics.  ...  sum of two primes.  ... 
arXiv:2108.05735v1 fatcat:yrpuc6jysndxxpknoo6cx2tctu

Modular curves and Mordell-Weil torsion in F-theory

Nadir Hajouji, Paul-Konstantin Oehlmann
2020 Journal of High Energy Physics  
We prove this by explicitly constructing and studying maps to a modular curve whose existence is predicted by a universal property.  ...  Article funded by SCOAP 3 . https://doi.org/10.1007/JHEP04(2020)103 JHEP04(2020)103 C Universal curves for Z 2 × Z 2m and Z m × Z 2m 42 C.1 Set-up 42 C.2 Construction 43 C.3 Z 2 × Z 4 44 7 For a more detailed  ...  Let p ⊂ R be a prime ideal and I ⊂ R an ideal. The order of vanishing of I at p is the largest integer m such that I ⊂ p m . Definition 5.6. Let φ = p q ∈ K, with p, q ∈ R relatively prime.  ... 
doi:10.1007/jhep04(2020)103 fatcat:ftimrypun5gbjj5h6gfwo4fkpe

Saturation, seminormalization and homeomorphisms of algebraic varieties [article]

François Bernard, Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
2022 arXiv   pre-print
We address the question under which conditions a bijective morphism between algebraic varieties over an algebraically closed field of characteristic zero is an isomorphism.  ...  Our two 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  ...  In order to study the saturation, we need to understand better the relation between prime ideals in A and B and prime ideals in B ⊗ A B.  ... 
arXiv:2203.09967v1 fatcat:g4d7ofkwibepxm776ptkadw4hi

Functorial affinization of Nash's manifold [article]

John Atwell Moody
2020 arXiv   pre-print
When there are infinitely many nonzero terms the sum should be taken formally or p-adically for a prime divisor p of n+2. There are finitely many nonzero terms if and only if C. D=0.  ...  If M is projective, singular foliations on M such that K+(n+1)H is a finitely-generated divisor of Iitaka dimension one are completely resolvable, where K is the canonical divisor of the foliation and  ...  Then W is an algebraic variety and Y 0 → M is not only a proper map, it is actualy the universal solution of resolving the indeterminacies of the rational map M− → W, ie it is the closure of the 'graph  ... 
arXiv:1004.2234v15 fatcat:ialjsgwly5avpl4xt25dcvyeqe

A uniform treatment of Grothendieck's localization problem [article]

Takumi Murayama
2021 arXiv   pre-print
To answer Grothendieck's problem, we provide a general framework that gives a uniform treatment of previously known cases of this problem, and also solves this problem in new cases, namely for weak normality  ...  Our proof of this statement reduces to a purely local question known as Grothendieck's localization problem.  ...  prime ideal p ⊆ A; and (b) We Definition 2.7 [ILO14, Exp.  ... 
arXiv:2004.06737v2 fatcat:3kwsw6ikgff35pbukmhoihbmry

Unpolarized Shafarevich conjectures for hyper-Kähler varieties [article]

Lie Fu, Zhiyuan Li, Teppei Takamatsu, Haitao Zou
2022 arXiv   pre-print
The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places.  ...  In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-K\"ahler varieties of CM type in a given deformation  ...  8.3 and Lemma A.3.  ... 
arXiv:2203.10391v1 fatcat:ty6z2foggnfcldg6u6jtgf5a5y

Modular Curves and Mordell-Weil Torsion in F-theory [article]

Nadir Hajouji, Paul-Konstantin Oehlmann
2019 arXiv   pre-print
We prove this by explicitly constructing and studying maps to a modular curve whose existence is predicted by a universal property.  ...  curves to explain the minimal singularities that appear on an elliptic fibration with prescribed torsion, and to determine the degree of the fundamental line bundle (hence the Kodaira dimension) of the universal  ...  Let m ⊂ R be a maximal ideal and I ⊂ R an ideal. The order of vanishing of I at m is the largest integer m such that I ⊂ m m . Definition 5.6. Let φ = p q ∈ K, with p, q ∈ R relatively prime.  ... 
arXiv:1910.04095v2 fatcat:p3italufbveb7gp5l2sjfzmojq

The Ando-Hopkins-Rezk orientation is surjective [article]

Sanath K. Devalapurkar
2020 arXiv   pre-print
We do so by constructing an E_1-ring B and a map B →MString such that the composite B →MString→tmf is surjective on homotopy.  ...  The universal property of A from Remark 2.5 therefore produces an E 1 -map A → BP.  ...  In this section, we show that this conjecture follows from Theorem 1.2. We begin by recalling the definition of the E ∞ -ring spectra M j r . Definition 6.1.  ... 
arXiv:1911.10534v3 fatcat:dhablqdo3bghtkrjv6a5wfojom

Terminal valuations and the Nash problem

Tommaso de Fernex, Roi Docampo
2015 Inventiones Mathematicae  
In dimension two, this result gives a new proof of the theorem of Fern\'andez de Bobadilla and Pe Pereira stating that, for surfaces, the Nash map is a bijection.  ...  Terminal valuations are defined in the sense of the minimal model program, as those valuations given by the exceptional divisors on a minimal model over X.  ...  The indeterminacies of S • (Z ′ ) • can be resolved by a minimal sequence Z • → S • of blow-ups of maximal ideals.  ... 
doi:10.1007/s00222-015-0597-5 fatcat:hcy2k2mqt5fwhg2kn2sgtxi5s4

The stable Adams conjecture and higher associative structures on Moore spectra [article]

Prasit Bhattacharya, Nitu Kitchloo
2021 arXiv   pre-print
Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the K-theory functor to a multi-natural transformation.  ...  More precisely, for any odd prime p, we show that M_p(k) admits a Thomified 𝔸_n-structure if and only if n < p^k. We also prove a weaker result for p=2.  ...  Thus, invoking Theorem 2.12 we produce a canonical null-homotopy which resolves Theorem 1.5 -the unreduced stable Adams conjecture. Definition 5.2.  ... 
arXiv:1803.11014v3 fatcat:pb5b6zypvbeolebyqt4cy337yy
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