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2013 Algebraization, Transcendence, and D-Group Schemes
Jean-Benoît Bost
Notre Dame J. Formal Logic 54(3-4): 377-434 (2013). DOI: 10.1215/00294527-2143961

Abstract

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 à la Schneider–Lang.

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Jean-Benoît Bost. "Algebraization, Transcendence, and D-Group Schemes." Notre Dame J. Formal Logic 54 (3-4) 377 - 434, 2013. https://doi.org/10.1215/00294527-2143961

Information

Published: 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1355.11074
MathSciNet: MR3091663
Digital Object Identifier: 10.1215/00294527-2143961

Subjects:
Primary: 11G35
Secondary: 11J81, 11J85, 12H05, 14B20, 14F40

Rights: Copyright © 2013 University of Notre Dame

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Vol.54 • No. 3-4 • 2013
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