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