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- Title
Homogeneous vector bundles over abelian varieties via representation theory.
- Authors
Brion, Michel
- Abstract
Let A be an abelian variety over a field. The homogeneous (or translation-invariant) vector bundles over A form an abelian category HVecA; the Fourier-Mukai transform yields an equivalence of HVecA with the category of coherent sheaves with finite support on the dual abelian variety. In this paper, we develop an alternative approach to homogeneous vector bundles, based on the equivalence of HVecA with the category of finite-dimensional representations of a commutative affine group scheme (the ''affine fundamental group'' of A). This displays remarkable analogies between homogeneous vector bundles over abelian varieties and representations of split reductive algebraic groups.
- Subjects
ABELIAN varieties; VECTOR bundles; REPRESENTATION theory; ABELIAN groups; ABELIAN categories; FUNDAMENTAL groups (Mathematics); SHEAF theory; AFFINE algebraic groups
- Publication
Representation Theory, 2020, Vol 24, p85
- ISSN
1088-4165
- Publication type
Article
- DOI
10.1090/ert/537