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Results tagged with cohomology
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user 39304
A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...
32
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2
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Etale cohomology can not be computed by Cech
It can be proven that if in a quasicompact scheme $X$ any finite subset is contained in an affine open subset then for any sheaf $\mathcal{F}$ on $X$ its Cech cohomology $\hat{H_{et}^{\bullet}}(X,\mathcal … {F})$ is naturally isomorphic to etale cohomology $H^{\bullet}_{et}(X,\mathcal{F})$. …
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11
votes
Accepted
Are the Eigenvalues of the Frobenius on Crystalline cohomology bounded by degree?
I assume that you mean $H^r_{crys}(X/W(k))$ because $H^r_{crys}(X/k)$ is just the de Rham cohomology over $k$. … In what follows, let us denote by $H^r$ the cohomology $H^r_{crys}(X/W(k))/torsion$. …
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4
votes
Accepted
A Tate-Sen theorem mod $p$
$\newcommand{\bQ}{\mathbb{Q}}\newcommand{\cO}{\mathcal{O}}\newcommand{\bC}{\mathbb{C}}\newcommand{\bZ}{\mathbb{Z}}\newcommand{\bF}{\mathbb{F}}$The open subgroup $Gal(\overline{\bQ}_p/\bQ_p(\mu_p))$ ac …
- 7,377
3
votes
Accepted
Examples of a group $G$ and an $F$-representation $V$ where $\cup:H^1(G,F)\otimes H^1(G,V)\t...
$\newcommand{\bZ}{\mathbb{Z}}$Let $G$ be a finite group of order divisible by $p:=\mathrm{char}\, F$ such that $\dim_F \mathrm{Hom}(G,F)\geq 2$ (e.g. $G=\bZ/p\times\bZ/p$). Take $V$ to be the kernel o …
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