Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 54, Number 3-4 (2013), 377-434.
Algebraization, Transcendence, and -Group Schemes
We present a conjecture in Diophantine geometry concerning the construction of line bundles over smooth projective varieties over . This conjecture, closely related to the Grothendieck period conjecture for cycles of codimension , is also motivated by classical algebraization results in analytic and formal geometry and in transcendence theory. Its formulation involves the consideration of -group schemes attached to abelian schemes over algebraic curves over . We also derive the Grothendieck period conjecture for cycles of codimension in abelian varieties over from a classical transcendence theorem à la Schneider–Lang.
Notre Dame J. Formal Logic, Volume 54, Number 3-4 (2013), 377-434.
First available in Project Euclid: 9 August 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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