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arXiv · 2310.16184

Shimura varieties

Sophie Morel
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Abstract

These are the notes of a course on Shimura varieties that I gave at the 2022 IHES summer school on the Langlands program. Lecture 1 gives an introduction to Shimura varieties over the complex numbers (defined here as a special type of locally symmetric spaces) and to the general theory of canonical models; it also discusses in more detail the example of the Siegel modular varieties. Lecture 2 presents some families of Shimura varieties (PEL type, Hodge type, abelian type) and the results that are known about their canonical and integral models. Finally, lecture 3 discusses the cohomology of Shimura varieties, concentrating mostly on the compact non-endoscopic case.

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Sophie Morel. 2023-10-24. Shimura varieties. https://arxiv.org/abs/2310.16184

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