Crystalline realizations of 1-motives

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.

54 pages, exposition improved, references & appendix added

References in corpus (2)

• Duality of Albanese and Picard 1-motives
• Albanese and Picard 1-motives

Cited by in corpus (11)

• Algebraization, transcendence, and D-group schemes
• Ogus realization of 1-motives
• The de Rham realization of the elliptic polylogarithm in families
• The filtered Ogus realisation of motives
• Perfect points of abelian varieties
• On deformations of $1$-motives
• A note on rank 1 log extendable isocrystals on simply connected open varieties
• Deligne's duality for de Rham realizations of 1-motives
• The Fontaine-Ogus realisation of Laumon 1-motives
• Motivic interpretation of Albanese varieties of smooth varieties
• Semistable abelian varieties and maximal torsion 1-crystalline submodules