All Questions
Tagged with galois-cohomology etale-cohomology
9 questions with no upvoted or accepted answers
8
votes
0
answers
157
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defining Selmer groups using étale cohomology
Concerning http://swc.math.arizona.edu/aws/1999/99RubinES.pdf, especially section I.5:
Can one define the Selmer groups and the unramified cohomology groups as étale
cohomology groups of certain ...
user19475
6
votes
0
answers
364
views
Galois invariants in étale cohomology
Suppose $X$ is a smooth projective variety over a field $k$, with separable closure $\overline{k}$, Galois group $G$, and let $\overline{X}$ be $X_{\overline{k}}$.
Do we have
$$(H^j(\overline{X},\...
user120812
3
votes
0
answers
152
views
Obtaining an exact sequence of Galois modules via derived functors
This question has two parts, the first part will be to obtain the desired exact sequence while the second will be to study it in the corresponding derived category and try to obtain it from there.
Let ...
- 895
3
votes
0
answers
243
views
Relation between Galois and etale cohomologies
Let $D$ be the ring of integers of a number field $F$.
Let $X=\mathrm{Spec} ~D$, and let $\pi$ be the etale fundamental group of $X$.
There are natural maps from $H^i(\pi, \mathbf{Z}/n)$ to $H^i_{...
- 367
2
votes
0
answers
70
views
Finite dimensionality of Galois cohomology
Let $K_S$ denote the maximal extension of $\mathbb{Q}$, unramified outside a finite set of primes $S$, and let $G_S$ denote the Galois group of $K_S/\mathbb{Q}$.
It is known that for any finitely ...
- 2,907
2
votes
0
answers
158
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Fundamental Group of small Zariski open set
Let $Y$ be an integral affine variety over $\mathbb{C}$ and $K$ be its function field. How to find a sufficiently small Zariski open set of $Y$ such that it is isomorphic to $K(\pi,1)$? Here $\pi$ is ...
- 677
2
votes
0
answers
264
views
etale cohomology of tori
Let $k$ be an algebraically closed field.
Let $A$ be a strictly henselian local ring which is a $k$-algebra.
Let $T$ a torus over $k((t))$.
Can we compute $H^{1}(A((t)),T)$?
- 3,472
1
vote
0
answers
170
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Galois cohomology of generic points of formal completions (of components of a hypercovering of the subvariety): examples or general statements?
Let $Y$ be a closed smooth subvariety in a (smooth) affine variety $X$. What can one say about the etale cohomology of the generic points of the formal completion of $X$ along $Y$ i.e. about the ...
- 16.9k
0
votes
0
answers
324
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Ordered Cech(-like) complexes that compute etale cohomology (of fields!)
It is well known (cf. Equivalence of ordered and unordered cech cohomology. ) that for 'usual' topologies one can compute the cohomology of sheaves either using unordered Cech complexes or ordered ...
- 16.9k