References about the Grothendieck's way of algebraizing the notions of calculus and differential geometry - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T09:36:37Z http://mathoverflow.net/feeds/question/100773 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100773/references-about-the-grothendiecks-way-of-algebraizing-the-notions-of-calculus-a References about the Grothendieck's way of algebraizing the notions of calculus and differential geometry kiseki 2012-06-27T13:02:50Z 2012-06-27T20:43:05Z <p>Hi everyone,</p> <p>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.... </p> <p>Are there any articles/books that deal with the the Grothendieck's way of algebraizing the notions of calculus and differential geometry?</p> <p>Thank you very much! </p> http://mathoverflow.net/questions/100773/references-about-the-grothendiecks-way-of-algebraizing-the-notions-of-calculus-a/100782#100782 Answer by Lars for References about the Grothendieck's way of algebraizing the notions of calculus and differential geometry Lars 2012-06-27T14:51:47Z 2012-06-27T14:51:47Z <p>Here are three references which were/are very helpful to me:</p> <ol> <li>Berthelot, Pierre; Ogus, Arthur: Notes on crystalline cohomology. </li> </ol> <p>Chapter 2 covers much of what you are looking for.</p> <ol> <li>Berthelot, Pierre: Cohomologie cristalline des schémas de caractéristique p>0. (French) Lecture Notes in Mathematics, Vol. 407</li> </ol> <p>Here, also chapter 2 contains many things you are looking for, in a more general setup.</p> <ol> <li>Grothendieck, Alexander: Crystals and the de Rham cohomology of schemes. 1968 Dix Exposés sur la Cohomologie des Schémas pp. 306–358</li> </ol> <p>This doesn't contain many details, but is still very interesting (certainly not only historically).</p>