Notre Dame Journal of Formal Logic

Algebraization, Transcendence, and D-Group Schemes

Jean-Benoît Bost

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.

Article information

Source
Notre Dame J. Formal Logic, Volume 54, Number 3-4 (2013), 377-434.

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1376053771

Digital Object Identifier
doi:10.1215/00294527-2143961

Mathematical Reviews number (MathSciNet)
MR3091663

Zentralblatt MATH identifier
1355.11074

Subjects
Primary: 11G35: Varieties over global fields [See also 14G25]
Secondary: 11J81: Transcendence (general theory) 11J85: Algebraic independence; Gelʹfond's method 12H05: Differential algebra [See also 13Nxx] 14B20: Formal neighborhoods 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]

Keywords
algebraization transcendence D-group schemes abelian schemes

Citation

Bost, Jean-Benoît. Algebraization, Transcendence, and $D$ -Group Schemes. Notre Dame J. Formal Logic 54 (2013), no. 3-4, 377--434. doi:10.1215/00294527-2143961. https://projecteuclid.org/euclid.ndjfl/1376053771


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