Homogeneous vector bundles over abelian varieties via representation theory - Archive ouverte HAL
Article Dans Une Revue Representation theory : An Electronic Journal of the American Mathematical Society Année : 2020

Homogeneous vector bundles over abelian varieties via representation theory

Michel Brion

Résumé

Let A be an abelian variety over a field. The homogeneous (or translation-invariant) vector bundles over A form an abelian category HVec A ; the Fourier-Mukai transform yields an equivalence of HVec A 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 HVec A 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.

Dates et versions

hal-04717969 , version 1 (02-10-2024)

Identifiants

Citer

Michel Brion. Homogeneous vector bundles over abelian varieties via representation theory. Representation theory : An Electronic Journal of the American Mathematical Society, 2020, 24 (3), pp.85-114. ⟨10.1090/ert/537⟩. ⟨hal-04717969⟩
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