English

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

Number Theory 2009-03-19 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.0903.3221,
  title  = {On Neron-Raynaud class groups of tori and the Capitulation Problem},
  author = {Cristian D. Gonzalez-Aviles},
  journal= {arXiv preprint arXiv:0903.3221},
  year   = {2009}
}

Comments

33 pages

R2 v1 2026-06-21T12:42:08.202Z