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

Abstract

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

22 pages

References in corpus (2)

• On the classification of quadratic forms over an integral domain of a global function field
• On the genera of semisimple groups defined over an integral domain of a global function field