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