Algebraization, transcendence, and D-group schemes

Abstract

We present a conjecture in Diophantine geometry concerning the construction of line bundles over smooth projective varieties over $\bar{\mathbb Q}}$. 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 $\bar{\mathbb Q}}$. We also derive the Grothendieck Period Conjecture for cycles of codimension 1 in abelian varieties over $\bar{\mathbb Q}}$ from a classical transcendence theorem à la Schneider-Lang.

To appear in the proceedings of the conference "Recent developments in model theory", Oléron 2011, in Notre Dame Journal of Formal Logic, Volume 54, Number 3-4, 2013. Typos corrected

References in corpus (3)

• Crystalline realizations of 1-motives
• Hermitian vector bundles and extension groups on arithmetic schemes. II. The arithmetic Atiyah extension
• Algebraic points on meromorphic curves

Cited by in corpus (5)

• Periods of Hodge structures and special values of the gamma function
• Motivic periods and Grothendieck arithmetic invariants
• Divisibility properties of motivic cohomology
• Elliptic KZB connections via universal vector extensions
• Moduli of rank 1 isocrystals