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Unipotent Schottky bundles on curves and abelian varieties

Thursday 16 December 2010 - Thomas Ludsteck

ARGOMENTI: Seminari

DAGA SEMINAR
Thomas Ludsteck (Stuttgart)
"Unipotent Schottky bundles on curves and abelian varieties"
Thursday, December 16, 2010, room 1BC50, h. 14:30

-Abstract
In a joint work with Carlos Florentino, we study a natural map from
representations of a free (resp. free abelian) group of rank g in GLr (C), to holomorphic vector bundles of degree 0 over a compact Riemann Surface X of genus g (resp. complex torus of dimension g). These free (resp. free abelian) groups are associated with Schottky uniformizations of X and are called Schottky groups. Our main result is that this natural map induces an equivalence of categories between the category of unipotent representations of Schottky groups, as well as the category of unipotent vector bundles on X. Finally we give an application to the p-adic case, where we show that for an algebraic p-adic torus there is an equivalence of categories between the category of integral and discrete representations of the temperate fundamental group, as well as the category of homogeneous vector bundles.

Rif. int. A. Bertapelle

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