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, Alexander (1966), Letter to J. Tate (PDF), archived from the original (PDF) on 2021-07-21.
• Grothendieck, Alexander (1968), "Crystals and the de Rham cohomology of schemes" (PDF), in Giraud, Jean; Grothendieck, Alexander; Kleiman, Steven L.; et al. (eds.), Dix Exposés sur la Cohomologie des Schémas, Advanced studies in pure mathematics, vol. 3, Amsterdam: North-Holland, pp. 306–358, MR 0269663, archived from the original (PDF) on 2022-02-08.
• 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.