185 citations · 736 across the 61 of their papers we have counts for
4 papers · 1 filter
Campana points, Vojta's conjecture, and level structures on semistable abelian varieties
Dan Abramovich, Anthony Várilly-Alvarado
We introduce a qualitative conjecture, in the spirit of Campana, to the effect that certain subsets of rational points on a variety over a number field, or a Deligne-Mumford stack…
Functorial factorization of birational maps for qe schemes in characteristic 0
Dan Abramovich, Michael Temkin
We prove functorial weak factorization of projective birational morphisms of regular quasi-excellent schemes in characteristic 0 broadly based on the existing line of proof for var…
Level structures on abelian varieties and Vojta's conjecture
Dan Abramovich, Keerthi Madapusi Pera, Anthony Várilly-Alvarado
Assuming Vojta's conjecture, and building on recent work of the authors, we prove that, for a fixed number field and positive integer , there is an integer such that f…
Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture
Dan Abramovich, Anthony Várilly-Alvarado
Assuming Lang's conjecture, we prove that for a fixed prime , number field , and positive integer , there is an integer such that no principally polarized abelian vari…