Why certain Tannaka groups attached to abelian varieties are almost connected

Abstract

We show that for a complex abelian variety X a certain Tannaka group G(X) attached to X is a pro-reductive group whose group of connected components is abelian, and hence isomorphic to the etale pro-finite abelian fundamental group of the dual abelian variety of X.

version 2: The main results now are shown also over finite fields and a new section 10 (classification of invertible objects) has been added. The previous appendix with its applications for the reference [W] has been deleted from the paper to become an appendix in [W] itself; besides that typos have been removed and the presentation has been partially improved

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• Brill-Noether Sheaves
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Cited by in corpus (4)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Degenerate Perverse Sheaves on Abelian Varieties
• Semisimple Super Tannakian Categories with a small Tensor Generator
• Vanishing theorems for abelian varieties over finite fields