A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
The complexity of equivalence for commutative rings

1990
*
Journal of symbolic computation
*

We study

doi:10.1016/s0747-7171(08)80053-3
fatcat:yn76kp2gabfubkwdrlmt6ej6ha
*the*deterministic time*complexity**of**the**equivalence*problems*for*formulas and*for*straight-line programs on*commutative**rings*. ... As corollaries*of*this theorem, we characterize*the*deterministic time*complexity**of*these two*equivalence*problems,*for*atl finite*commutative**rings*and*for*all*commutative*unitary*rings**of*zero or prime ... Preliminary versions*of*some*of*these results were presented at*the*Fifth International Conference on Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Menorca, Spain, June 1987. ...##
###
The homotopy theory of complete modules
[article]

2020
*
arXiv
*
pre-print

Given a

arXiv:2011.06989v1
fatcat:vyqsy44l7rf6roxqfduwdfxv4y
*ring*homomorphism R → S, we then give necessary and sufficient conditions*for**the*categories*of*complete R-*complexes*and*the*categories*of*complete S-*complexes*to have*equivalent*homotopy theories ... Given a*commutative**ring*R and finitely generated ideal I, one can consider*the*classes*of*I-adically complete, L_0^I-complete and derived I-complete*complexes*. ...*For*a*commutative**ring*R and an ideal I, we fix*the*following notation: • Ch(R) denotes*the*category*of*(unbounded) chain*complexes**of*R-modules; • Ch(R, I) denotes*the*category*of**complexes**of*I-adically ...##
###
Genuine-commutative ring structure on rational equivariant K-theory for finite abelian groups
[article]

2021
*
arXiv
*
pre-print

This means that every genuine-

arXiv:2104.01079v1
fatcat:c22a5kmqfjgfjnyftqeensg7ye
*commutative**ring*spectrum whose homotopy groups are those*of*KU_ℚ,G is weakly*equivalent*, as a genuine-*commutative**ring*spectrum, to KU_ℚ,G. ... In contrast,*the*connective rational equivariant K-theory spectrum does not have this type*of*uniqueness*of*genuine-*commutative**ring*structure. ... We also thank Mike Hill*for*many useful conversations and Christian Wimmer*for*sharing a draft*of*his work.*The*first author thanks Spencer Dowdall*for*acting as a notational soundingboard. ...##
###
Cochains and homotopy type

2006
*
Publications mathématiques (Bures-sur-Yvette)
*

*The*cochain functor from

*the*homotopy category

*of*finite type nilpotent spaces to

*the*homotopy category

*of*E-infinity algebras is faithful but not full. ... Finite type nilpotent spaces are weakly

*equivalent*if and only if their singular cochains are quasi-isomorphic as E-infinity algebras. ...

*For*

*commutative*

*ring*coefficients, expect some kind

*of*

*ring*structure.

*For*

*commutative*

*ring*coefficients, expect some kind

*of*

*ring*structure. ...

##
###
An algebraic model for commutative Hℤ–algebras

2017
*
Algebraic and Geometric Topology
*

We show that

doi:10.2140/agt.2017.17.2013
fatcat:jqjigera4bbfznbsyzwzcda4n4
*the*homotopy category*of**commutative*algebra spectra over*the*Eilenberg-Mac Lane spectrum*of**the*integers is*equivalent*to*the*homotopy category*of*E-infinity-monoids in unbounded chain*complexes*... We also provide a Quillen*equivalence*to*commutative*monoids in*the*category*of*functors from*the*category*of*finite sets and injections to unbounded chain*complexes*. ... Mike Mandell showed in [M03, 7.11 ] that*for*every*commutative**ring*R*the*homotopy categories*of*E ∞ -HR-algebra spectra and*of*E ∞ monoids in*the*category*of*unbounded R-chain*complexes*are*equivalent*...##
###
Totally acyclic complexes

2017
*
Journal of Algebra
*

Thus we improve slightly on a result

doi:10.1016/j.jalgebra.2016.09.009
fatcat:gtrlapwu7ngibeuijrnvqttwni
*of*Iyengar's and Krause's; in [22] they proved that*for*a*commutative*noetherian*ring*R with a dualizing*complex*,*the*class*of*acyclic*complexes**of*injectives coincides ... We prove (Corollary 1) that, over a*commutative*noetherian*ring*R,*the**equivalent*statements in Theorem 3 hold if and only if*the**ring*is Gorenstein. ... Thus R is an Iwanaga-Gorenstein*ring*. ...##
###
Local Gorenstein duality in chromatic group cohomology
[article]

2021
*
arXiv
*
pre-print

We consider local Gorenstein duality

arXiv:2106.08669v2
fatcat:ixkbfs2llbbtfmtgzqa37dmf3q
*for*cochain spectra C^*(BG;R) on*the*classifying spaces*of*compact Lie groups G over*complex*orientable*ring*spectra R. ... We show that it holds systematically*for*a large array*of*examples*of**ring*spectra R, including Lubin-Tate theories, topological K-theory, and various forms*of*topological modular forms. ... By a*complex*oriented*commutative**ring*spectrum we always mean a*commutative**ring*spectrum with an E 1 -*complex*orientation. ...##
###
THE COMPLEXITY OF THE EQUIVALENCE PROBLEM OVER FINITE RINGS

2011
*
Glasgow Mathematical Journal
*

In this paper we investigate

doi:10.1017/s001708951100053x
fatcat:wsaerkkpjndjffq35h543ylfla
*the*computational*complexity**of**the**equivalence*problem*for*finite*rings*. ... We investigate*the**complexity**of**the**equivalence*problem over a finite*ring*when*the*input polynomials are written as sum*of*monomials. ... Theorem 3 establishes polynomial time*complexity**for*an abundant class*of**rings**for*which R/J is*commutative*. COROLLARY 4. ...##
###
Derived equivalences between associative deformations

2010
*
Journal of Pure and Applied Algebra
*

*The*main result

*of*

*the*paper (Theorem 2.7) says that if T is a two-sided tilting

*complex*over B-A relative to K, then T ∼ = P [n]

*for*some invertible bimodule P and integer n. ... Introduction Let K be a

*commutative*

*ring*, and let A and B be associative unital K-algebras. We denote by Mod A and Mod B

*the*corresponding categories

*of*left modules. ... I wish to thank Bursztyn and Waldmann

*for*explaining their work to me, and

*the*organizers

*of*

*the*conference

*for*providing

*the*background

*for*this interaction. ...

##
###
Derived completions in stable homotopy theory
[article]

2007
*
arXiv
*
pre-print

We construct a notion

arXiv:0707.2585v1
fatcat:6yrjbo37nnh6rnbm4f7v7ri5ty
*of*derived completion which applies to homomorphisms*of**commutative*S-algebras. ... We study*the*relationship*of**the*construction with other constructions*of*completions, and prove various invariance properties. ...*The*case*of**rings**For*any*ring*A, we may construct*the*Eilenberg-MacLane spectrum H(A). ...##
###
Commutative ring spectra
[article]

2017
*
arXiv
*
pre-print

*The*notion

*of*etale extensions in

*the*spectral world is tricky and we explain why. We define Picard groups and Brauer groups

*of*

*commutative*

*ring*spectra and present examples. ... As a first interesting class

*of*examples

*of*such

*ring*spectra we focus on (

*commutative*) algebra spectra over

*commutative*Eilenberg-MacLane

*ring*spectra. ... Then there is a chain

*of*Quillen

*equivalences*between

*the*model category

*of*

*commutative*HR-algebra spectra and E ∞monoids in

*the*category

*of*unbounded R-chain

*complexes*. ...

##
###
Formal groups and stable homotopy of commutative rings

2004
*
Geometry and Topology
*

We show that formal group laws account

doi:10.2140/gt.2004.8.335
fatcat:jhu57cpgwfhfpep56x2nyth5ei
*for*all such*ring*spectrum maps, and we identify*the*space*of**ring*spectrum maps between HZ and DB. ... We study a*ring*spectrum denoted DB which depends on a*commutative**ring*B and is closely related to*the*topological Andre-Quillen homology*of*B. ... Something similar happens*for*Gamma-*rings*. Suppose R is a Gamma-*ring*which is stably*equivalent*to an algebra over*the**commutative*Gamma-*ring*k . ...##
###
Duality in algebra and topology

2006
*
Advances in Mathematics
*

*rings*

*of*finite groups, (4) Poincaré duality

*for*groups and (5) Gross-Hopkins duality in chromatic stable homotopy theory as examples

*of*a single phenomenon. ... This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality

*for*manifolds, (2) Gorenstein duality

*for*

*commutative*

*rings*, (3) Benson-Carlson duality

*for*cohomology ... From this point

*of*view S plays

*the*role

*of*

*the*ground

*ring*

*for*

*the*category

*of*spectra, just as Z is

*the*ground

*ring*

*for*

*the*category

*of*chain

*complexes*. Mapping spectra. ...

##
###
On the relationship between logarithmic TAQ and logarithmic THH
[article]

2021
*
arXiv
*
pre-print

*The*latter is analogous to results

*of*Weibel-Geller

*for*Hochschild homology

*of*discrete

*rings*, and

*of*McCarthy-Minasian and Mathew

*for*topological Hochschild homology. ... We provide a new description

*of*logarithmic topological Andr\'e-Quillen homology in terms

*of*

*the*indecomposables

*of*an augmented

*ring*spectrum. ...

*For*example,

*the*above result applies

*for*

*the*augmented

*commutative*symmetric

*ring*spectrum A → THH(A) → A

*for*A connective. ...

##
###
Spectra for commutative algebraists
[article]

2006
*
arXiv
*
pre-print

*The*article is designed to explain to

*commutative*algebraists what spectra (in

*the*sense

*of*algebraic topology) are, why they were originally defined, and how they can be useful

*for*

*commutative*algebra ... Just as any derived

*equivalence*

*of*

*rings*is given by tensoring with a

*complex*

*of*bimodules, any Quillen

*equivalence*between

*ring*spectra is given by smashing with a bimodule spectrum [28] . ...

*The*best known example is that

*of*Morita

*equivalence*, showing that a

*ring*is derived

*equivalent*to

*the*

*ring*

*of*n × n matrices over it. ...

« Previous

*Showing results 1 — 15 out of 92,572 results*