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Homogeneous vector bundles over abelian varieties via representation theory

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Michel Brion
Université Grenoble Alpes
Fre, 2018-11-23 09:00 - 10:00
MPIM Lecture Hall

Let $A$ be an abelian variety over a field. The homogeneous (or translation-invariant) vector bundles over $A$ form an abelian category; the Fourier-Mukai transform yields an equivalence of this category with that of coherent sheaves with finite support on the dual abelian variety. The talk will present an alternative approach to the category of homogeneous vector bundles, based on an equivalence 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.

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