Results 1 to 10 of about 4,804 (72)

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

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, Gutiérrez, Javier J.   +1 more
core   +2 more sources

Enriched $\infty$-operads

, 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

Centralizers in good groups are good [PDF]

, 2014
We modify the transchromatic character maps to land in a faithfully flat extension of Morava E-theory. Our construction makes use of the interaction between topological and algebraic localization and completion.
Barthel, Tobias, Stapleton, Nathaniel
core   +1 more source

Completed representation ring spectra of nilpotent groups

, 2009
In this paper, we examine the `derived completion' of the representation ring of a pro-p group G_p^ with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg ...
Carlsson, Carlsson, Elmendorf, Hovey, Lubotzky, Nunley, Schwede, Tyler Lawson   +7 more
core   +1 more source

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, Naumann, Niko, Noel, Justin   +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, Beilinson, Blumberg, Bunke, Bunke, Bunke, Burgos, Day, Deligne, Deligne, Drew, Déglise, Feliu, Gepner, Gepner, Gillet, Glasman, Holmstrom, Jardine, Joyal, Lurie, Lurie, Mazel-Gee, Morel, Naumann, Nikolaus, Peters, Robalo, Spitzweck, Weibel   +29 more
core   +1 more source

Logarithmic structures on topological K-theory spectra

, 2013
We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the respective periodic spectra.
Sagave, Steffen
core   +1 more source

Dimension functions for spherical fibrations

, 2018
Given a spherical fibration $\xi$ over the classifying space $BG$ of a finite group we define a dimension function for the $m-$fold fiber join of $\xi$ where $m$ is some large positive integer. We show that the dimension functions satisfy the Borel-Smith
Okay, Cihan, Yalcin, Ergun
core   +2 more sources