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, 3-4pm in MIT room E17-136.
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Fall 2013 topic: p-adic geometry, focusing on adic and perfectoid spaces

From September 27 on, the main references for this seminar will be Scholze, Perfectoid spaces and Wedhorn, Adic spaces.

September 6: Bjorn Poonen. Overview and organizational meeting.
September 13: Nathan Harman. "Naive" p-adic manifolds. (This is independent of the theory of adic spaces, but is sufficient for many applications.) References: Serre, Classification des variétés analytiques p-adiques compactes, Topology 3 (1965), 409-412 [copyrighted: for MIT use only]. Also, Chapter III of Part II of Serre, Lie algebras and Lie groups, 1965.
September 20: Dmitry Vaintrob. Survey of rigid analytic geometry. (To some extent, adic spaces are a modern replacement for rigid spaces, so we will discuss rigid spaces only briefly.) References: Sections 1 and 2 of Conrad, Several approaches to non-archimedean geometry. For a briefer introduction, see Section 3 of Papikian, Rigid-analytic geometry and the uniformization of abelian varieties.
September 27: Ruthi Hortsch. (Semi)valuations: ordered abelian groups, Q_p-bar, C_p, examples of spherically complete fields, examples of valuations of rank > 1. References: Pages 7 and 8 of Scholze, Perfectoid spaces, and Chapters 1 and 2 of Wedhorn, Adic spaces. Also see Poonen, Maximally complete fields, Enseign. Math. (2) 39 (1993), no. 1-2, 87–106 and the references cited there for some examples of spherically complete fields.
October 4: NO MEETING (math department retreat)
October 11: David Corwin. Valuation spectra: definition of Spv A, spectral spaces. References: Chapter 4 (and a few definitions from Chapter 3) of Wedhorn, Adic spaces or Section 2 of Huber, Continuous valuations, Math. Z. 212 (1993), 455-477.
October 18: Kęstutis Česnavičius. f-adic rings and Tate rings. References: Chapter 6 (and a few definitions from Chapter 5) of Wedhorn, Adic spaces.
October 25: NO MEETING (AGNES at Boston College)
November 1: Yihang Zhu. The adic spectrum of an affinoid ring. Reference: Chapter 7 of Wedhorn, Adic spaces. See also Chapter 2 of Scholze, Perfectoid spaces.
November 8: Sug Woo Shin. Adic spaces. Reference: Chapter 8 of Wedhorn, Adic spaces.
November 15: Lukas Brantner. Formal schemes as adic spaces. Reference: Chapter 9 of Wedhorn, Adic spaces.
November 22: Zhuo Chen. Perfectoid fields. Reference: Chapter 3 of Scholze, Perfectoid spaces.
November 29: NO MEETING (Thanksgiving break)
December 6: Chao Li. Almost mathematics. Reference: Chapter 4 of Scholze, Perfectoid spaces. For more details, see Chapters 2 and 3 of Gabber and Ramero, Almost ring theory.

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

Organizers: Jennifer Park and Bjorn Poonen