Results 1 to 10 of about 4,763 (38)
Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces [PDF]
, 2015 We construct a new spectrum of units for a commutative symmetric ring spectrum that detects the difference between a periodic ring spectrum and its connective cover. It is augmented over the sphere spectrum.
Boardman +11 more
core +2 more sources
The smooth Whitehead spectrum of a point at odd regular primes [PDF]
, 2003 Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described.
Adams +32 more
core +5 more sources
Hyperdescent and \'etale K-theory
, 2021 We study the \'etale sheafification of algebraic K-theory, called \'etale K-theory. Our main results show that \'etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently,
Clausen, Dustin, Mathew, Akhil
core +1 more source
Cosimplicial resolutions and homotopy spectral sequences in model categories [PDF]
, 2003 We develop a general theory of cosimplicial resolutions, homotopy spectral sequences, and completions for objects in model categories, extending work of Bousfield-Kan and Bendersky-Thompson for ordinary spaces. This is based on a generalized cosimplicial
Bousfield, A K
core +1 more source
Braided injections and double loop spaces [PDF]
, 2015 We consider a framework for representing double loop spaces (and more generally E-2 spaces) as commutative monoids. There are analogous commutative rectifications of braided monoidal structures and we use this framework to define iterated double ...
Schlichtkrull, Christian +1 more
core +1 more source
Morita homotopy theory for $(\infty,1)$-categories and $\infty$-operads [PDF]
, 2019 We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty,1)$-categories and $\infty$-operads.
Caviglia, Giovanni +1 more
core +2 more sources
, 2019 In this paper we initiate the study of enriched $\infty$-operads. We introduce several models for these objects, including enriched versions of Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and Moerdijk, and show these are ...
Chu, Hongyi, Haugseng, Rune
core +1 more source
Localizations and completions in motivic homotopy theory
, 2018 Let $K$ be a perfect field and let $E$ be a homotopy commutative ring spectrum in the Morel-Voevodsky stable motivic homotopy category $\mathcal{SH}(K)$. In this work we investigate the relation between the $E$-homology localization and $E$-nilpotent completion of a spectrum X.
openaire +5 more sources
Nilpotence and descent in equivariant stable homotopy theory
, 2016 Let $G$ be a finite group and let $\mathscr{F}$ be a family of subgroups of $G$. We introduce a class of $G$-equivariant spectra that we call $\mathscr{F}$-nilpotent.
Mathew, Akhil +2 more
core +1 more source
The Beilinson regulator is a map of ring spectra
, 2018 We prove that the Beilinson regulator, which is a map from $K$-theory to absolute Hodge cohomology of a smooth variety, admits a refinement to a map of $E_\infty$-ring spectra in the sense of algebraic topology.
Barwick +29 more
core +1 more source