2
votes
0answers
304 views

What are the easiest cases of base change (for sheaves on sites)?

I have a closed embedding of schemes $i:X'\to X$, and for each of them I consider three Grothendieck topologies for the category of the corresponding (relatively) \'etale schemes: the \'etale one, the ...
3
votes
1answer
681 views

Cohomologie Etale

Is there an English translation available for Deligne's Cohomologie Etale (Arcata) that is now part of the SGA 4 1/2 ?? Atleast for the first two sections - Grothendieck Topologies and Etale Topology. ...
10
votes
2answers
1k views

Locally constant sheaves for the étale topology, lack of intuition about “étale-localness”

I have started studying some ├ętale cohomology and I am trying to build up some intuition about the concept of local for the ├ętale topology. I can understand some nice examples (like Kummer exact ...
11
votes
1answer
685 views

Motivic cohomology with finite coefficients for singular varieties

Let $X$ be a smooth variety over a field $K$ whose characteristic does not divide a positive integer $m$. Then the motivic cohomology of $X$ with coefficients in $\mathbb Z/m(j)$ can be computed in ...
1
vote
1answer
703 views

Zariski sheaves lifted to etale topology

Let $X$ be a "reasonable" scheme (I am particularly interested in smooth algebraic varieties over a field). Let $Zar_X$ denote the (small) Zariski site of (open subschemes of) $X$ and $Et_X$ denote ...