Seminar on Crystalline Cohomology, Columbia 2018

This seminar met on Tuesdays from 4:30 - 6:00 in room 622. The seminar was organized by Brian Lawrence and Shizhang Li.

Crystalline cohomology is a p-adic cohomology theory for smooth, proper varieties in characteristic p. Our goal will be to understand the construction and basic properties of crystalline cohomology. Topics will depend on interest but may include the de Rham - Witt complex, rigid comohology or the interaction of Frobenius and the Hodge filtration.

References (more to be added)

Illusie, L. (1975). Report on crystalline cohomology. In: Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) (pp. 459–478). Amer. Math. Soc., Providence, R.I.
Ogus, A. (1975). Cohomology of the infinitesimal site. Ann. Sci. École Norm. Sup. (4), 8(3), 295–318.
Berthelot, P., & Ogus, A. (1978). Notes on crystalline cohomology. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo.
Illusie, L. (1994). Crystalline cohomology. In: Motives (Seattle, WA, 1991) (pp. 43–70). Amer. Math. Soc., Providence, RI.
Bhatt, B and de Jong, A. J. (2011). Crystalline cohomology and de Rham cohomology.
de Jong, A. J. (Unpublished) On a result of Artin.

Schedule of talks

Date	Speaker	Title
January 23	Brian Lawrence	Introduction
January 30	Shizhang Li	Divided Powers and Crystalline Cohomology
February 6	Shizhang Li	Crystalline Site, Crystalline Cohomology, de Rham Cohomology
February 13	Yogesh	Crystals (Berthelot & Ogus, 6.1-6.10)
February 20	Raymond Cheng	Poincaré Lemma (Berthelot & Ogus, 6.12)
February 27	Brian Lawrence	Dieudonné-Manin Classification
March 6	David Hansen	Bhatt-de Jong (Crystalline - de Rham Comparison)
March 20	Daniel Gulotta	Frobenius is an Automorphism
March 27	David Hansen	De Rham-Witt Complex
April 10	David Hansen	P-adic Hodge Theory and a Comparison Isomorphism
April 17	Yihang Zhu	P-Divisible Groups and Grothendieck-Messing I
April 24	Yihang Zhu	P-Divisible Groups and Grothendieck-Messing II

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