## Seminar on Crystalline Cohomology, Columbia 2018 |
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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- de Jong, A. J. (Unpublished) On a result of Artin.

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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