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

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

2009-03-18

arxiv.org/abs/0903.3221v1

Mathematics

Number Theory

33 pages

Scientific paper

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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