In mathematics, infinitesimal cohomology is a cohomology theory for algebraic varieties introduced by Grothendieck (1966). In characteristic 0 it is essentially the same as crystalline cohomology. In nonzero characteristic p Ogus (1975) showed that it is closely related to etale cohomology with mod p coefficients, a theory known to have undesirable properties.
References
Grothendieck, A. (1966), Letter to J. Tate (PDF)
Grothendieck, Alexander (1968), "Crystals and the de Rham cohomology of schemes", in Giraud, Jean; Grothendieck, Alexander; Kleiman, Steven L.; et al. (eds.), Dix Exposés sur la Cohomologie des Schémas (PDF), Advanced studies in pure mathematics, 3, Amsterdam: North-Holland, pp. 306–358, MR 0269663
Ogus, Arthur (1975). "Cohomology of the infinitesimal site". Annales scientifiques de l'École Normale Supérieure. 8 (3): 295–318. doi:10.24033/asens.1289. MR 0422280.
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