Tangential localization for Selmer varieties

Author: 

Kim, M

Journal: 

Duke Mathematical Journal

Publication Date: 

2012

Last Updated: 

2018-09-07T18:02:21.827+01:00

Issue: 

2

DOI: 

10.1215/00127094-1507332

Volume: 

161

page: 

173-199

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 . 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.

Symplectic id: 

310620

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article