Shimura varieties
Number Theory
2023-11-07 v2
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.
Keywords
Cite
@article{arxiv.2310.16184,
title = {Shimura varieties},
author = {Sophie Morel},
journal= {arXiv preprint arXiv:2310.16184},
year = {2023}
}
Comments
64 pages, to appear in Proceedings of Symposia in Pure Mathematics