Abelian class groups of reductive group schemes

Abstract

We introduce the abelian class group C_{ab}(G) of a reductive group scheme G over a ring A of arithmetical interest and study some of its properties. In particular, we show that if the fraction field of A is a global field without real primes, then there exists a surjection C(G)-->> C_{ab}(G), where C(G) is the class set of G.

33 pages. Final version accepted for publication

References in corpus (3)

• Le défaut d'approximation forte dans les groupes linéaires connexes
• Théorèmes de dualité pour les complexes de tores
• Flasque resolutions of reductive group schemes

Cited by in corpus (1)

• A building-theoretic approach to relative Tamagawa numbers of quasi-split semisimple groups over global function fields