Infinitesimal cohomology

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, https://agrothendieck.github.io/divers/LGT66scan.pdf .
• Grothendieck, Alexander (1968), "Crystals and the de Rham cohomology of schemes", in Giraud, Jean; Grothendieck, Alexander; Kleiman, Steven L. et al., Dix Exposés sur la Cohomologie des Schémas, Advanced studies in pure mathematics, 3, Amsterdam: North-Holland, pp. 306–358, https://agrothendieck.github.io/divers/CRCSscan.pdf .
• Ogus, Arthur (1975). "Cohomology of the infinitesimal site.". Annales scientifiques de l'École Normale Supérieure 8 (3): 295–318. doi:10.24033/asens.1289.