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arXiv · 1307.4783

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

David Harari·Claus Scheiderer·Tamás Szamuely
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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.

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David Harari, Claus Scheiderer, Tamás Szamuely. 2014-01-27. Weak approximation for tori over $p$-adic function fields. https://arxiv.org/abs/1307.4783

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