Deformations and derived categories
Copyright policy )Deformations and derived categories
In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology of μ p on certain affine CM ellitpic curves.
- University of Pennsylvania United States
- University of Iowa United States
Ordinary representations and characters, Galois representations, Deformations and infinitesimal methods in commutative ring theory, CM elliptic curves, Infinitesimal methods in algebraic geometry, Derived categories, triangulated categories, Abelian varieties of dimension \(> 1\), Spectral sequences, hypercohomology, versal deformations, derived categories, hypercohomology, Elliptic curves over global fields, Limits, profinite groups, universal deformations
Ordinary representations and characters, Galois representations, Deformations and infinitesimal methods in commutative ring theory, CM elliptic curves, Infinitesimal methods in algebraic geometry, Derived categories, triangulated categories, Abelian varieties of dimension \(> 1\), Spectral sequences, hypercohomology, versal deformations, derived categories, hypercohomology, Elliptic curves over global fields, Limits, profinite groups, universal deformations
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