Classification of Shimura varieties

Abstract: Primarily cover Chapters 6-8 of Milne.

Remind us of the definition of a Shimura datum, and maybe give SV2*-SV6 on p.63. Sketch the construction of the Siegel modular variety in Chapter 6 and why it satisfies SV1-SV6. Show that the Siegel modular variety parametrizes polarized abelian varieties over $\mathbb{C}$ with symplectic level structure.

Summarize Hodge type Shimura varieties as in Chapter 7.

If you have time, sketch what changes to go from Siegel modular varieties to PEL Shimura varieties (Chapter 8). It would be great to cover some idea of Shimura varieties of abelian type (Chapter 9).

algebraic geometrynumber theory

Audience: advanced learners

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STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning 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.

Fall 2025 topic: Weil conjectures.

Some topics 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.

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