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The twisted forms of a semisimple group over a Hasse domain of a global function field | | Rony A. Bitan
; Ralf Kohl
; Claudia Schoemann
; | | Date: |
14 Nov 2018 | | Abstract: | Let $K=mathbb{F}_q(C)$ be the global field of rational functions on a smooth
and projective curve $C$ defined over a finite field $mathbb{F}_q$. Any finite
but non-empty set $S$ of closed points on $C$ gives rise to a Hasse integral
domain $mathcal{O}_S=mathbb{F}_q[C-S]$ of $K$. Given a semisimple and
almost-simple group scheme $underline{G}$ defined over $ ext{Spec}
mathcal{O}_S$ with a smooth fundamental group $F(underline{G})$, we aim to
describe the set of ($mathcal{O}_S$-classes of) twisted-forms of
$underline{G}$ in terms of some invariants of $F(underline{G})$ and the
absolute type of the Dynkin diagram of $underline{G}$. This turns out
sometimes to biject to a disjoint union of abelian groups. | | Source: | arXiv, 1811.5723 | | Services: | Forum | Review | PDF | Favorites | |
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