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 Mondays, 4pm-5:30pm, with a short break in the middle, in MIT room 2-449 (not online!), unless indicated otherwise below.
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 2023 topic: Shimura varieties.
The whole subject is generalizing the pages of [Ser] cited above,
so consider reading those pages before the seminar 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.
- [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).
- [GN] Genestier and Ngo, Lectures on Shimura varieties.
- [Int] Milne, Introduction to Shimura varieties.
- [Tra] Deligne, Travaux de Shimura, English translation (similar goals, but more terse: assumes that the reader already knows a lot of background).
- [Lan] Lan, An example-based introduction to Shimura varieties.
- [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), English translation (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).
Some topics below might take more or less time than allotted.
If a speaker runs out of time on a certain date, that speaker might be
allowed to borrow some time on the next date. So the topics below might not
line up exactly with the dates below.
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, Spring 2016, Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022