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Preprint Number 553

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553. Jean-Benoit Bost
Algebraization, transcendence, and D-group schemes
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Submission date: 17 January 2013.

Abstract:

(To appear in the proceedings of the conference Recent developments in model theory, Oléron 2011)
We present a conjecture in Diophantine geometry concerning the construction of line bundles over smooth projective varieties over Q. This conjecture, closely related to the Grothendieck Period Conjecture for cycles of codimension 1, is also motivated by classical algebraization results in analytic and formal geometry and in transcendence theory. Its formulation involves the consideration of D-group schemes attached to abelian schemes over algebraic curves over Q. We also derive the Grothendieck Period Conjecture for cycles of codimension 1 in abelian varieties over Q from a classical transcendence theorem a la Schneider-Lang.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1301.4102: pdf, ps.


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