Shimura Varieties and Moduli - James Milne

Shimura Varieties and MilneApril 30, 2011, Shimura Varieties are the quotients of hermitian symmetric domainsby discrete groups defined by congruence conditions. We examine their relation withmoduli ..41 Elliptic modular curves5 Definition of elliptic modular curves ..5 Elliptic modular curves as Moduli Varieties ..62 Hermitian symmetric domains9 Preliminaries on Cartan involutions and polarizations ..9 Definition of hermitian symmetric domains ..10 Classification in terms of real groups ..11 Classification in terms of root systems ..12 Example: the Siegel upper half space ..133 Discrete subgroups of Lie groups14 Lattices in Lie groups ..14 Arithmetic subgroups of algebraic groups ..15 Arithmetic lattices in Lie groups ..16 Congruence subgroups of algebraic groups ..184 Locally symmetric varieties18 Quotients of hermitian symmetric domains ..18 The algebraic structure on the quotient ..19 Chow s theorem.

Shimura Varieties and Moduli J.S. Milne April 30, 2011, v2.00 Abstract Connected Shimura varieties are the quotients of hermitian symmetric domains

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  Varieties, Moduli, Shimura, Shimura varieties and moduli

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