The twisted forms of a semisimple group over an \(\mathbb{F}_q\)-curve. (English. French summary) Zbl 1507.11057
Summary: Let \(C\) be a smooth, projective and geometrically connected curve defined over a finite field \(\mathbb{F}_q\). 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 \(F(\underline{G})\).
MSC:
| 11G20 | Curves over finite and local fields |
| 11G45 | Geometric class field theory |
| 11R29 | Class numbers, class groups, discriminants |
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