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searching for Sheaf of modules 6 found (17 total)

Generic flatness (393 words) [view diff] exact match in snippet view article find links to article

flatness and generic freeness state that under certain hypotheses, a sheaf of modules on a scheme is flat or free. They are due to Alexander Grothendieck

Flat vector bundle (417 words) [view diff] exact match in snippet view article find links to article

_{X}^{*}(E)=\Omega _{X}^{*}\otimes E} denote the vector space (in fact a sheaf of modules over O X {\displaystyle {\mathcal {O}}_{X}} ) of differential forms

Cotangent bundle (1,472 words) [view diff] exact match in snippet view article find links to article

{I}}/{\mathcal {I}}^{2}\right).} By Taylor's theorem, this is a locally free sheaf of modules with respect to the sheaf of germs of smooth functions of M. Thus it

Crystal (mathematics) (844 words) [view diff] exact match in snippet view article

isomorphism. This is similar to the definition of a quasicoherent sheaf of modules in the Zariski topology. An example of a crystal is the sheaf O X /

Tensor contraction (1,882 words) [view diff] exact match in snippet view article find links to article

complex manifold, analytic space, or scheme. Let M be a locally free sheaf of modules over OX of finite rank. Then the dual of M is still well-behaved and

Crystalline cohomology (1,922 words) [view diff] exact match in snippet view article find links to article

isomorphism. This is similar to the definition of a quasicoherent sheaf of modules in the Zariski topology. An example of a crystal is the sheaf OX/S