Abelian class groups of reductive group schemes

2011/08/16 by Cristian D. Gonzalez-Aviles, Cristian D. González-Avilés, Gonzalez-Aviles, Cristian D. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1108.3264

33 pages. Final version accepted for publication

openalex publication_date 2011/08/16 · arxiv created 2012/02/18 · arxiv updated 2012/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Théorèmes de dualité pour les complexes de tores

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