Crystalline realizations of 1-motives, by F. Andreatta and L. Barbieri Viale

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 Picard 1-motive, over perfect fields.

This paper is in part a fitting sequel to the following:

F. Andreatta <>
L. Barbieri Viale <>