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Integral points on surfaces and the Chabauty-Kim method.

Lundi, 2 Avril, 2007 - 16:00
Prénom de l'orateur : 
Nom de l'orateur : 
Résumé : 

Recently, M. Kim has given a new proof of (a special case of) Siegel's theorem on integral points on curves. His method is a nonabelian version of the classical Chabauty method. Briefly, one constructs p-adic analytic functions on the curve, as iterated integrals, which vanish on the set of integral points.
In joint work with Tamas Szamuely, we are trying to adept this method to higher dimension in order to prove the following conjecture:
Conjecture: Let X be the complement in P^2 of a normal crossing divisor of degree at least 4. Let R be a subring of Q, finitely generated over Z. Then the set of R-integral points on X is not Zariski dense.
This is a special case of the Lang-Vojta conjecture(s). In my talk I would like to explain the main ideas behind the Chabauty-Kim method, and to report on our recent progress towards proving the above conjecture.

Institution de l'orateur : 
Université de Heidelberg (Allemagne
Thème de recherche : 
Algèbre et géométries
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