English

Why certain Tannaka groups attached to abelian varieties are almost connected

Algebraic Geometry 2015-10-27 v3

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.

Keywords

Cite

@article{arxiv.1207.4039,
  title  = {Why certain Tannaka groups attached to abelian varieties are almost connected},
  author = {Rainer Weissauer},
  journal= {arXiv preprint arXiv:1207.4039},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-21T21:37:08.397Z