September 7: Algebraic de Rham cohomology and the Gauss-Manin connection (Grothendieck and Katz-Oda). Define hypercohomology and algebraic de Rham cohomology, and use GAGA to prove that for a smooth projective complex variety it agrees with classical de Rham cohomology. Recall the definition of connection, explain the algebraic definition of the Gauss-Manin connection in terms of differentiating k-forms, prove that relative Betti cohomology is horizontal. |
September 14: Review of étale cohomology (Milne). The étale site, definition of étale cohomology and l-adic cohomology, statement of comparison with Betti cohomology for a smooth projective complex variety, Weil conjectures, bad behavior of p-adic cohomology of varieties in characteristic p. |
September 21: NO MEETING? (MIT student holiday) |
September 28: Crystalline cohomology (Chambert-Loir, I.1 and I.2) |
October 5: Summary of p-adic Hodge theory (Illusie up to 2.2, Berger II.4) |
October 12: |
October 19: |
October 26: |
November 2: |
November 9: |
November 16: |
November 23: NO SEMINAR (Thanksgiving Break) |
November 30: |
December 7: |
December 14: |
Organizers: Borys Kadets, Bjorn Poonen, Zhiwei Yun, Wei Zhang