Weak approximation for tori over $p$-adic function fields
Number Theory
2014-01-28 v2 Algebraic Geometry
Abstract
This is the companion piece to "Local-global questions for tori over p-adic function fields" by the first and third authors. We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field, the main focus here being weak approximation of rational points. We construct a 9-term Poitou--Tate type exact sequence for tori over a field as above (and also a 12-term sequence for finite modules). Like in the number field case, part of the sequence can then be used to analyze the defect of weak approximation for a torus. We also show that the defect of weak approximation is controlled by a certain subgroup of the third unramified cohomology group of the torus.
Cite
@article{arxiv.1307.4783,
title = {Weak approximation for tori over $p$-adic function fields},
author = {David Harari and Claus Scheiderer and Tamás Szamuely},
journal= {arXiv preprint arXiv:1307.4783},
year = {2014}
}
Comments
final version, to appear in IMRN