The Stacks project

Example 36.6.11. Let $X = \mathop{\mathrm{Spec}}(A)$ be affine, $f_1, \ldots , f_ c \in A$, and let $\mathcal{F} = \widetilde{M}$ for some $A$-module $M$. The map $c_{f_1, \ldots , f_ c}$ of Remark 36.6.10 can be described as the map

\[ M/(f_1, \ldots , f_ c)M \longrightarrow \mathop{\mathrm{Coker}}\left( \bigoplus M_{f_1 \ldots \hat f_ i \ldots f_ c} \to M_{f_1 \ldots f_ c} \right) \]

sending the class of $s \in M$ to the class of $s/f_1 \ldots f_ c$ in the cokernel.

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  • 3 comment(s) on Section 36.6: Cohomology with support in a closed subset

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View Example 36.6.11 as pdf