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for questions about etale cohomology of schemes, including foundational material and applications.

17 votes
Accepted

Why does a group action on a scheme induce a group action on cohomology?

If a (say constant) group $G$ acts on a scheme $X$, you may want to consider the notion of a $G$-sheaf : a sheaf $\mathcal F$ endowed with isomorphisms $\lambda_g: g^* \mathcal F\simeq \mathcal F$, fo …
Niels's user avatar
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9 votes
Accepted

On a quasi-separated assumption in a lemma for the homotopy exact sequence of the etale fund...

This is more a comment than an answer: a few years back, in 2011, while working with some friends on SGA1, we also found out that we could not prove this statement without the hypothesis that $X$ is q …
Niels's user avatar
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2 votes

Group cohomology of fundamental group of a curve

The best thing you could do in my opinion is to have a look at Appendix A Algebraic $K(\pi, 1)$ Spaces in Stix, Jakob Projective anabelian curves in positive characteristic and descent theory …
Niels's user avatar
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1 vote

Weights for etale cohomology: why does Deligne's definition work?

It seems that your question is not well defined unless $K$ is finitely generated over its prime field. See for instance Jannsen, Uwe Weights in arithmetic geometry. Jpn. J. Math. 5 (2010), no. 1, 73–1 …
Niels's user avatar
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