On Neron-Raynaud class groups of tori and the Capitulation Problem

2009/03/18 by Gonzalez-Aviles, Cristian D.
#11R99 #20G30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0903.3221

Abstract

We discuss the Capitulation Problem for Neron-Raynaud class groups of tori over global fields F and obtain generalizations of the main results of [10]. We also show that short exact sequences of F-tori induce long exact sequences involving the corresponding Neron-Raynaud class groups. For example, we show that the Neron-Raynaud class group of any F-torus which is split by a metacyclic extension of F can be "resolved" in terms of classical ideal class groups of global fields.

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