Seminar on Topics in Arithmetic, Geometry, Etc.

STAGE is a seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.
Meetings are held on Fridays, 4-5pm in MIT room E17-136.
To receive announcements by email, add yourself to the STAGE mailing list.

Spring 2014 topics: perfectoid spaces, Weil II

The main references for this seminar will be Scholze, Perfectoid spaces and Katz, L-functions and monodromy: four lectures on Weil II.

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.

Additional resources:
Past semesters: Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013. For semesters up to and including Spring 2009, see the old STAGE webpage.

Organizers: Kęstutis Česnavičius and Bjorn Poonen