Campana points, Vojta's conjecture, and level structures on semistable abelian varieties

@article{Abramovich2016CampanaPV,
  title={Campana points, Vojta's conjecture, and level structures on semistable abelian varieties},
  author={Dan Abramovich and Anthony V{\'a}rilly-Alvarado},
  journal={arXiv: Number Theory},
  year={2016}
}
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 over a ring of S-integers, cannot be Zariski dense. The conjecture interpolates, in a way that we make precise, between Lang's conjecture for rational points on varieties of general type over number fields, and the conjecture of Lang and Vojta that asserts that S-integral points on a variety of logarithmic general… Expand
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References

SHOWING 1-9 OF 9 REFERENCES
Level structures on abelian varieties and Vojta’s conjecture
Assuming Vojta’s conjecture, and building on recent work of the authors, we prove that, for a fixed number field $K$ and a positive integer $g$ , there is an integer $m_{0}$ such that for anyExpand
Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture
Assuming Lang's conjecture, we prove that for a fixed prime $p$, number field $K$, and positive integer $g$, there is an integer $r$ such that no principally polarized abelian variety $A/K$ ofExpand
Fibres multiples sur les surfaces: aspects geométriques, hyperboliques et arithmétiques
We show the hyperbolic and complex function field versions of Lang’s conjecture for smooth projective surfaces S having a fibration f:S→C with orbifold base an orbifold curve of general type. TheExpand
Birational geometry for number theorists
Awfully idiosyncratic lecture notes from CMI summer school in arithmetic geometry July 31-August 4, 2006. Does not include: rationality problems, techniques of the minimal model problem and much ofExpand
A more general abc conjecture
This note formulates a conjecture generalizing both the abc conjecture of Masser-Oesterl\'e and the author's diophantine conjecture for algebraic points of bounded degree. It also shows that the newExpand
Hom-stacks and restriction of scalars
Fix an algebraic space S, and let X and Y be separated Artin stacks of finite presentation over S with finite diagonals (over S). We define a stack HomS(X ,Y) classifying morphisms between X and Y.Expand
Degeneration of Abelian varieties
I. Preliminaries.- II. Degeneration of Polarized Abelian Varieties.- III. Mumford's Construction.- IV. Toroidal Compactification of Ag.- V. Modular Forms and the Minimal Compactification.- VI.Expand
Diophantine geometry, volume 201 of Graduate Texts in Mathematics
  • 2000
Diophantine geometry, volume 201 of Graduate Texts in Mathematics
  • 2000