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Results tagged with cohomology
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user 297229
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, ...
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Base change of cohomology when the cohomology is a torsion
Let $\mathscr F$ be a coherent sheaf such that $H^i(X,\mathscr F)$ is a torsion for $i>0$, i.e. the $i$-th cohomology of $\mathscr F$ on the generic fiber vanishes. … $X_k$, and assume $\mathscr F$ is locally free, then we have the exact sequence
$$0\rightarrow \mathscr F\otimes \mathscr I\rightarrow \mathscr F\rightarrow \mathscr F|_{X_k}\rightarrow 0,$$
Applying cohomology …
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