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Mathematische Annalen

, Volume 331, Issue 1, pp 111–172 | Cite as

Crystalline realizations of 1-motives

  • Fabrizio Andreatta
  • Luca Barbieri-VialeEmail author
Article

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 (formal) liftings to zero characteristic. We then show that one dimensional crystalline cohomology of an algebraic variety, defined by forcing universal cohomological descent via de Jong’s alterations, coincides with the crystalline realization of the Picard 1-motive, over perfect fields of characteristic >2.

Keywords

Algebraic Variety Positive Characteristic Comparison Theorem Perfect Field Crystalline Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità degli Studi di PadovaPadovaItaly
  2. 2.Dipartimento di Metodi e Modelli MatematiciUniversità degli Studi di Roma La SapienzaRomaItaly

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