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Results tagged with etale-cohomology
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user 4008
for questions about etale cohomology of schemes, including foundational material and applications.
6
votes
Accepted
Relationship between topological cohomology and $\ell$-adic cohomology
The way to study the topology of the situation was introduced by Khovanski in
"Newton polyhedra, and toroidal varieties" Funkcional. Anal. i Priložen. 11
(1977), no. 4, 56--64, 96. His result (if I ha …
- 22.6k
8
votes
Accepted
Exact sequence in étale cohomology related with proper birational morphism
Let $V := X\setminus E$ and $U := Y\setminus D$ and $j\colon U \rightarrow Y$ and
$k\colon V \rightarrow X$ the inclusions. We have exact sequences
$\cdots\rightarrow H^\ast(X,k_!\mathbb Z_\ell)\right …
- 22.6k
11
votes
Accepted
Leray-Hirsch principle for étale cohomology
[[ I have added a discussion of when $p$ is smooth or has quotient singularities. ]]
[[ I added a discussion on the cohomology of $[X/G]$. ]]
The étale case follows in a way that is altogether analog …
- 22.6k
5
votes
If one wants to work with $Q_l$-adic sheaves, should the scheme be of finite type over a 1-d...
At the time of the writing of the 'Adic formalism' the complete finiteness and the formalism of all the relevant operators was only known for the case mentioned (I think that SGA 4 1/2 was the most co …
- 22.6k
2
votes
Accepted
For an l-adic sheaf (F_n), why is the complex F_n of finite Tor dimension?
I think you have (slightly) misread your sources. If you take Rapport
for instance (which is the one I am familiar with) Deligne never make this claim
(as far as I can see). As a typical example consi …
- 22.6k