English

Crystalline realizations of 1-motives

Algebraic Geometry 2007-05-23 v2 Number Theory

Abstract

We consider the crystalline realization of Deligne's 1-motives in positive characteristics and prove a comparison theorem with the De Rham realization of liftings to zero characteristic. We then show that one dimensional crystalline cohomology of an algebraic variety, defined by universal cohomological descent via de Jong's alterations, coincide with the crystalline realization of the (cohomological) Picard 1-motive, over perfect fields.

Keywords

Cite

@article{arxiv.math/0302161,
  title  = {Crystalline realizations of 1-motives},
  author = {Fabrizio Andreatta and Luca Barbieri Viale},
  journal= {arXiv preprint arXiv:math/0302161},
  year   = {2007}
}

Comments

54 pages, exposition improved, references & appendix added