Crystalline realizations of 1-motives

Details Crystalline realizations of 1-motives Crystalline realizations of 1-motives

2003-02-13

arxiv.org/abs/math/0302161v2

Mathematische Annalen Vol. 331, N. 1, (2005) 111-172

Mathematics

Algebraic Geometry

54 pages, exposition improved, references & appendix added

Scientific paper

10.1007/s00208-004-0576-4

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.

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