Goal: Learning Shimura varieties is hard. This seminar aims to give a basic introduction and stream-lined overview of Shimura varieties, their examples and their geometry. We will be going through Milne's notes, including canonical models, reflex fields and good reductions of Shimura varieties.
In particular, we will try to be as hands-on as possible and have some concrete examples in our pocket. I do not foresee this but if time permits, I can present some topics that are more directly related to my research (i.e. local models of Shimura varieties, Bruhat-Tits group schemes, orbital integrals, etc.).
Speaker: I will give all of the talks and provide all of the notes, unless you would like to volunteer of course!
Space-time coordinates: Tuesday, 9:30am-11am, Math lounge
Schedule:
(24th Jan) Hermitian symmetric domains (notes)
(31st Jan) Hodge structures and polarizations (notes)
(7th Feb) Parametrizing Hodge structures (notes)
(14th Feb) Locally symmetric varieties, Baily-Borel compactification (notes)
Notable References: Viviani's notes, Goresky's notes, Pmac's notes,
"Smooth compactifications of locally symmetric varieties" by Ash, Mumford, Rapoport, Tai.
(21st Feb) Working out examples of locally symmetric varieties
(28th Feb) Connected Shimura varieties (notes)
(7th March) Spring break.
(14th March) Shimura varieties (notes)
(21st March) Siegel modular variety (notes)
(28th March)
(4th April) No seminar. I'm at a conference.
(11th April)
(18th April)
(25th April)
In case you were wondering:
To give a sense of how Shimura varieties relate to my research, I'm trying to understand these papers:
T. Haines: Introduction to Shimura varieties with bad reduction of parahoric type (link)
T. Haines & N.B. Chau: Nearby cycles for local models of some Shimura varieties (link)
G. Pappas & X. Zhu: Local models of Shimura varieties and a conjecture by Kottwitz (link)
M. Kisin & G. Pappas: Integral models of Shimura varieties with parahoric level structure (link)