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- Title
Torseurs sous une variété abélienne sur R((t)).
- Authors
Ducros, Antoine
- Abstract
Let V be an henselian discrete valuation ring with real closed residue field and let k be its quotient ring; we denote by k + and k − the two real closures of k. Consider a k-abelian variety A. We compute the Galois-cohomology group H 1( k, A) in terms of the reduction of the dual variety of A and of the semi-algebraic topology of A( k +) and A( k −). The tools we need are Ogg's results concerning valuation rings with algebraically closed residue field, Hochschild–Serre spectral sequence and Scheiderer's local-global principles. At the end we study more precisely the case of an elliptic curve.
- Publication
Manuscripta Mathematica, 2001, Vol 105, Issue 3, p311
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s002290100183