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Results tagged with local-cohomology
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user 22810
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Relation between local cohomology and open immersions
This is true. The functor $RHom(\mathcal{O}_X/\mathcal{I}^{n+1},-)$ is in fact a different name for $j^!$ when $j: Z_n \to X$. Where $Z_n$ is the $n$-truncated formal neighborhood of $Z$ in $X$. In th …
- 7,799
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Relation between local cohomology and open immersions
Let $X$ be a noetherian scheme $U \subset X$ an open subset with complement $Z = X- U$. Assume $Z$ is cut out by the ideal sheaf $\mathcal{I} \subset \mathcal{O}_X$. We have exact sequences:
$$0 \to …
- 7,799