Download E-books Lectures on Hilbert Modular Varieties and Modular Forms (Crm Monograph Series) PDF

By Eyal Z. Goren

This ebook is dedicated to sure features of the idea of $p$-adic Hilbert modular types and moduli areas of abelian kinds with genuine multiplication. the idea of $p$-adic modular kinds is gifted first within the elliptic case, introducing the reader to key rules of N. M. Katz and J.-P. Serre. it really is re-interpreted from a geometrical viewpoint, that is built to offer the rudiments of the same conception for Hilbert modular kinds. the idea of moduli areas of abelian types with genuine multiplication is gifted first very explicitly over the complicated numbers. points of the overall idea are then uncovered, particularly, neighborhood deformation thought of abelian forms in confident attribute. The mathematics of $p$-adic Hilbert modular types and the geometry of moduli areas of abelian types are similar. This relation is used to review $q$-expansions of Hilbert modular types, at the one hand, and stratifications of moduli areas nonetheless. The e-book is addressed to graduate scholars and non-experts. It makes an attempt to supply the mandatory historical past to all recommendations uncovered in it. it could actually function a textbook for a sophisticated graduate direction.

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