Weak Approximation for Tori Over p-adic Function Fields
| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Harari, David; Scheiderer, Claus; Szamuely, Tamás |
| Year of publication: | 2015 |
| Published in: | International Mathematics Research Notices : IMRN ; 2015, 10. - pp. 2751-2783. - ISSN 1073-7928. - eISSN 1687-0247 |
| ArXiv-ID: | arXiv:1307.4783 |
| DOI (citable link): | https://dx.doi.org/10.1093/imrn/rnu019 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Bibliography of Konstanz: | Yes |
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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(10), pp. 2751-2783. ISSN 1073-7928. eISSN 1687-0247. Available under: doi: 10.1093/imrn/rnu019
@article{Harari2015Appro-26404, title={Weak Approximation for Tori Over p-adic Function Fields}, year={2015}, doi={10.1093/imrn/rnu019}, number={10}, issn={1073-7928}, journal={International Mathematics Research Notices : IMRN}, pages={2751--2783}, author={Harari, David and Scheiderer, Claus and Szamuely, Tamás} }
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