February 7: Jessica Fintzen. Perfectoid algebras. Reference: Chapter 5 of Scholze, Perfectoid spaces. |
February 14: Yunqing Tang. The cotangent complex. Reference: Stacks Project, Tag 08P5 and Chapter 5 of Scholze, Perfectoid spaces. |
February 21: NO MEETING (MSRI workshop on perfectoid spaces) |
February 28: NO MEETING |
March 7: Padmavathi Srinivasan. Statement of the weight monodromy conjecture, including some preparatory material: Grothendieck's l-adic monodromy theorem, monodromy operator and existence of monodromy filtrations (including some properties, namely, primitive decomposition and/or tensors of monodromy filtrations), interpretation of the conjecture. Reference: The beginning of Chapter 9 of Scholze, Perfectoid spaces. The statement is in 9.3/9.4/9.6, and the interpretation is in the paragraph below 9.3. |
March 14: NO MEETING (Arizona Winter School) |
March 21: Koji Shimizu. The equal characteristic weight monodromy conjecture. (The goal is to sketch Deligne's proof.) Reference: Paragraph below 9.4 in Scholze, Perfectoid spaces. |
March 28: NO MEETING (Spring Break) |
April 4: Sug Woo Shin. The mixed characteristic weight monodromy conjecture for hypersurfaces. Reference: Theorem 9.6 in Scholze, Perfectoid spaces. |
April 11: John Binder. Introduction to Weil II: weights, formulation of main theorem, corollaries. Reference: Up to the top of page 9 in Katz, L-functions and monodromy: four lectures on Weil II. |
April 18: Kęstutis Česnavičius. Artin-Schreier sheaf, purity theorem. Reference: Page 9 to the middle of page 15 in Katz, L-functions and monodromy: four lectures on Weil II. |
April 25: David Corwin. Reduction of the main theorem to the purity theorem, statement of the monodromy theorem. Reference: Page 15 to the middle of page 20 in Katz, L-functions and monodromy: four lectures on Weil II. |
May 2: Koji Shimizu. Reduction of the purity theorem to the monodromy theorem. Reference: Page 20 to the middle of page 26 in Katz, L-functions and monodromy: four lectures on Weil II. |
May 9: Yunqing Tang. Proof of the monodromy theorem. Reference: Pages 26-35 in Katz, L-functions and monodromy: four lectures on Weil II. |
May 16 at 1pm in E17-129: Chao Li. Applications of the main theorem: Weil I, geometric semisimplicity, Hard Lefschetz, function-field Sato-Tate, Ramanujan conjecture. Reference: Page 36 to the end of Katz, L-functions and monodromy: four lectures on Weil II. |
Organizers: Kęstutis Česnavičius and Bjorn Poonen