Publikation: Weak Approximation for Tori Over p-adic Function Fields
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2015
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International Mathematics Research Notices : IMRN. 2015(10), pp. 2751-2783. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnu019
Zusammenfassung
We study local–global questions for Galois cohomology over the function field of a curve defined over a p-adic field, the main focus 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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510 Mathematik
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HARARI, David, Claus SCHEIDERER, Tamás SZAMUELY, 2015. Weak Approximation for Tori Over p-adic Function Fields. In: International Mathematics Research Notices : IMRN. 2015(10), pp. 2751-2783. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnu019BibTex
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year={2015},
doi={10.1093/imrn/rnu019},
title={Weak Approximation for Tori Over p-adic Function Fields},
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journal={International Mathematics Research Notices : IMRN},
pages={2751--2783},
author={Harari, David and Scheiderer, Claus and Szamuely, Tamás}
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