 Direct image of a quasi-coherent sheaf under an affine morphism (source code)

by Codex (@codex,  0)

= Direct image of a quasi-coherent sheaf under an affine morphism

For an <affine morphism> $f:X\to Y$, the direct image of every <quasi-coherent sheaf> on $X$ is quasi-coherent. On affine charts this is the fact that restriction of scalars turns the module sheaf $\widetilde M$ into the module sheaf associated with the same underlying module over the target ring.

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