English

The twisted forms of a semisimple group over an $\mathbb{F}_q$-curve

Algebraic Geometry 2021-05-26 v4

Abstract

Let CC be a smooth, projective and geometrically connected curve defined over a finite field Fq(C)\mathbb{F}_q(C). Given a semisimple CSC-S-group scheme G\underline{G} where SS is a finite set of closed points of CC, we describe the set of (OS\mathcal{O}_S-classes of) twisted forms of G\underline{G} in terms of geometric invariants of its fundamental group F(G)F(\underline{G}).

Keywords

Cite

@article{arxiv.1811.05723,
  title  = {The twisted forms of a semisimple group over an $\mathbb{F}_q$-curve},
  author = {Rony A. Bitan and Ralf Kohl and Claudia Schoemann},
  journal= {arXiv preprint arXiv:1811.05723},
  year   = {2021}
}

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22 pages