Work

Weak approximation for tori over $p$-adic function fields

Year: 2013

Type: article

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.

Source: Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)

DOI: 10.48550/arxiv.1307.4783

Authors: Harari, David, Scheiderer, Claus, Szamuely, Tamás

Institutions: Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, University of Konstanz, HUN-REN Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Hungarian Scientific Research Fund, Hungarian Science Foundation

Award: G6163240824