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0
votes
1answer
177 views

Descend of etale morphism

I am not sure whether the title is appropriate for this question or not. I am sorry if there is anyone who is confused with the title and the contents. What I want to ask is the following: let $k$ be ...
7
votes
1answer
185 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 ...
8
votes
0answers
148 views

Stack of Tannakian categories? Galois descent?

I'm having trouble finding a reference for something that I'm guessing the experts worked out long ago. Let's take a local or global field $F$ for this post, and fix a separable algebraic closure ...
0
votes
0answers
148 views

Descent for group actions

Suppose I have a finite Galois extension of fields $K/k$, as well as a finite group $G$ with a surjection $f: G \rightarrow \mathrm{Gal}(K/k)$. Finally, suppose I have an action $\sigma$ of $G$ on a ...
1
vote
1answer
290 views

Galois descent for semilinear endomorphisms

Let $K \subset L$ be a finite Galois extension, $\sigma$ an automorphism of $L$ (not necessarily fixing $K$) and let $E$ be a finite-dimensional vector space over $L$ together with an $\sigma$-linear ...
5
votes
3answers
801 views

Applications of Descent?

The technique of faithfully flat descent, and, in the case of vector spaces, Galois descent has been used quite a bit in Algebraic Geometry. However, the question of whether, say, a given $k$-vector ...
4
votes
1answer
271 views

Reference wanted - etale sheaves on $X$ versus on $\overline{X}$

Hello, Let $X$ be a scheme of finite type over a field $k$. Let $l$ be an Galois extension of $k$ with Galois group $\Gamma$, and $\overline{X}$ be the base change of $X$ from $k$ to $l$. Then If I ...
5
votes
1answer
784 views

What kind of structures allow Galois descent?

EDIT: Question solved. Let me explain what I mean. The classical formulation of Galois descent, e. g. in Crawley-Boevey's "Cohomology and central simple algebras", uses the following notion: ...
4
votes
4answers
581 views

Galois descent, explicit inverse map

Let $L/K$ be a finite Galois extension with Galois group $G$ and $V$ a $L$-vector space, on which $G$ acts by $K$-automorphisms satisfying $g(\lambda v)=g(\lambda) g(v)$. It is known that the ...