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Results tagged with deformation-theory
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user 39304
for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
5
votes
Flatness of direct image sheaf over local artinian ring
$\newcommand{\C}{\mathbb{C}}\newcommand{\D}{\C[t]/t^2}\newcommand{\im}{\mathrm{im}\,}$A module $M$ over $\D$ is flat if and only if the inclusion $(t)\subset \D$ remains injective after tensoring with …
- 7,377
4
votes
Accepted
Push-forward of flat module under a finite, flat morphism
Yes, it follows from the projection formula https://stacks.math.columbia.edu/tag/08EU For any $A$-module $M$ we have $$Rf_{A*}\mathcal{F}_A\otimes^{L}_{\mathcal{O}_Y}p^*M\simeq Rf_{A*}(\mathcal{F}_A\o …
- 7,377