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Hi everyone,

I'm looking for some references about the differential operators on schemes(connection, curvature, etc...). I am reading the EGA IV 16, but EGA does not treats connection, curvature, etc....

Are there any articles/books that deal with the the Grothendieck's way of algebraizing the notions of calculus and differential geometry?

Thank you very much!

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There in no (currently known) straightforward way of defining the curvature of a scheme. There was a question some time back about curvature in algebraic geometry... –  Steven Gubkin Jun 27 '12 at 13:31
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up vote 6 down vote accepted

Here are three references which were/are very helpful to me:

  1. Berthelot, Pierre; Ogus, Arthur: Notes on crystalline cohomology.

Chapter 2 covers much of what you are looking for.

  1. Berthelot, Pierre: Cohomologie cristalline des schémas de caractéristique p>0. (French) Lecture Notes in Mathematics, Vol. 407

Here, also chapter 2 contains many things you are looking for, in a more general setup.

  1. Grothendieck, Alexander: Crystals and the de Rham cohomology of schemes. 1968 Dix Exposés sur la Cohomologie des Schémas pp. 306–358

This doesn't contain many details, but is still very interesting (certainly not only historically).

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Thanks so much Lars! –  kiseki Jun 27 '12 at 14:57
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