Shimura data and Shimura varieties

Abstract: Primarily cover Chapter 4-5 of Milne.

Define congruence subgroup and relate to compact open subgroups of $G(\mathbb{A}_f)$, no proofs necessary. Define connected Shimura datum, equivalence via Prop. 4.8. Proposition 4.9. Define connected Shimura variety. Cover Example 4.14 on Hilbert modular varieties. Give the adelic description in Prop 4.18 and Prop 4.19.

Remind us of $G^{\mathrm{der}}$ and $G^{\mathrm{ad}}$. Define Shimura datum, compare to connected Shimura datum. Give Ex 5.6. Cover Prop 5.7, Cor 5.8, Prop 5.9. Define Shimura varieties. Define a morphism of Shimura varieties.

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.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

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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