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6 votes
1 answer
560 views

Higher descent cohomology

Descent cohomology for a comonad is defined at degrees 0 and 1 by Mesablishvili in his paper "On Descent Cohomology" (as well as by many other authors in many other contexts). For a comonad $\bot$ on ...
7 votes
1 answer
498 views

Basic example of derived descent

I've been trying to understand the Adams spectral sequence, and I've gotten myself confused about how derived descent is supposed to work, so I would like to understand a simple example. Given a ...
4 votes
0 answers
253 views

Homotopy colimit description of stacks

Let $F$ be an Artin stack. If $p: X \to F$ is an atlas for $F$, can we express $F$, in the $\infty$-category ${\rm Shv}^{\acute{et}}(k)$ of higher stacks, as a homotopy colimit over the simplicial ...
5 votes
0 answers
225 views

Does the Amitsur complex have a universal property?

The question is essentially the title. In other words, is there some universal property that the Amitsur complex for a morphism of rings $\phi:A\to B$ satisfies as a cosimplicial ring, or cosimplicial ...
7 votes
1 answer
526 views

Which morphisms of ring spectra are of effective descent for modules?

There is a well understood bifibration of $\infty$-categories over the $\infty$-category of commutative ring spectra whose fiber over a ring $R$ is the category of $R$-module spectra. This is in ...