Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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!

share|improve this question
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
add comment

1 Answer

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).

share|improve this answer
Thanks so much Lars! –  kiseki Jun 27 '12 at 14:57
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.