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 Tuesdays, 9-10:30am in MIT room 2-135.
To receive announcements by email, add yourself to the STAGE mailing list.
If you are interested in giving one of the talks, please contact the organizers.

Spring 2016 topic: Shimura varieties.

References:

[Ser] Serre, A course in arithmetic, pages 77-84 (prerequisite material on a quotient of the upper half plane as the moduli space of elliptic curves over C).
[What] Milne, What is a Shimura variety? (3-page introduction).
[SV] Milne, Shimura variety (one-page encyclopedia entry).
[Int] Milne, Introduction to Shimura varieties (we will mainly follow this). Here are some comments on the notes.
[Tra] Deligne, Travaux de Shimura (similar goals, but more terse: assumes that the reader already knows a lot of background).
[Kne] Kneser, Semi-simple algebraic groups, Chapter X in Cassels and Fröhlich, Algebraic number theory.
[Voi] Voisin, Hodge theory and complex algebraic geometry I, Chapter 7 (Hodge theory background, with more details than in Chapter 2 of [Int]).
[Var] Deligne, Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques, pages 247-289 in Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII (1979) (sequel to [Tra] that extends the construction of canonical models from the case of Hodge type to the case of abelian type).
[Kot] Kottwitz, Points on some Shimura varieties over finite fields (for the PEL case).
[Lan] Lan, Arithmetic compactifications of PEL-type Shimura varieties, Princeton University Press, 2013.
[Mod] Milne, Shimura varieties and moduli.
[Mot] Milne, Shimura varieties and motives (explains the moduli interpretation of abelian-type Shimura varieties mentioned in Section 9 of [Int]).
[Act] Milne, The action of an automorphism of C on a Shimura variety and its special points (constructs canonical models for general Shimura varieties).

The whole subject is generalizing the pages of [Ser] cited above, so you should read those pages before the semester begins if you are not already familiar with that basic material. You might read [What] and [SV] too, to get a sense of what the subject is about.

February 2: Borys Kadets: Reductive groups in characteristic 0 (tori, semisimple groups, simply connected and adjoint groups, Hasse principle, strong approximation theorem, real approximation theorem, Dynkin diagrams, Cartan involutions, restriction of scalars). References: Section 1 of [Kne], pages 125-126 of [Tra], and pages 17-19 of [Int].

February 9: Chi-Yun Hsu: Hermitian symmetric domains (Chapter 1 of [Int])

February 16 in 2-139: Isabel Vogt: Hodge structures and their classifying spaces (Chapter 2 of [Int], Chapter 7 of [Voi])

February 23: Yuzhou Gu: Locally symmetric varieties (Chapter 3 of [Int])

March 1: Lynnelle Ye: Connected Shimura varieties (Chapter 4 of [Int])

March 8: Zijian Yao: Shimura varieties (Chapter 5 of [Int])

March 15: NO SEMINAR (Arizona Winter School)

March 22: NO SEMINAR (Spring Break)

March 29: Nicholas Triantafillou: The Siegel Modular Variety (Chapter 6 of [Int])

April 5: Geoffrey Smith: Shimura varieties of Hodge and PEL type (Chapters 7 and 8 of [Int])

April 12: Lynnelle Ye: Complex Multiplication (Chapters 10 and 11 of [Int])

April 19: NO SEMINAR (Patriots Day)

April 26: Atticus Christensen: Canonical Models I

May 3: Chi-Yun Hsu: Canonical Models II

May 10: Zijian Yao: Integral Models of Shimura Varieties

Past semesters: Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015, Fall 2015. For semesters up to and including Spring 2009, see the old STAGE webpage.

Organizers: David Corwin, Naoki Imai, and Bjorn Poonen