1 February 2012 Tangential localization for Selmer varieties
Minhyong Kim
Duke Math. J. 161(2): 173-199 (1 February 2012). DOI: 10.1215/00127094-1507332

Abstract

This paper proposes a tangential version of the theory of Selmer varieties together with a formulation of cohomological duality in families of Lie algebras indexed by nonabelian cohomology. This theory allows one to consider deformations of cohomology classes as one moves over the Selmer variety and suggests an approach for generalizing to number fields the homotopical techniques for proving Diophantine finiteness that were developed over Q. The utility of this perspective is demonstrated by way of a new proof of Siegel’s theorem on finiteness of S-integral points for the projective line minus three points over a totally real field.

Citation

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Minhyong Kim. "Tangential localization for Selmer varieties." Duke Math. J. 161 (2) 173 - 199, 1 February 2012. https://doi.org/10.1215/00127094-1507332

Information

Published: 1 February 2012
First available in Project Euclid: 19 January 2012

zbMATH: 1268.11079
MathSciNet: MR2876929
Digital Object Identifier: 10.1215/00127094-1507332

Subjects:
Primary: 11G05

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 2 • 1 February 2012
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