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Assume that $X$ is a proper smooth variety over an algebraically closed field $k$, $U=X\setminus (\cup D_i))$ where $D_i$ are closed subvarieties such that the set-theoretic intersections of all sets ...

Let $x$ be a nonzerodivisor on a local Noetherian ring $(R,m).$ Let $M,N$ be finitely generated $R/xR$-modules. How to show the existence of the following exact sequence $\cdots\longrightarrow ...