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.
Read Online or Download Lectures on Hilbert Modular Varieties and Modular Forms (Crm Monograph Series) PDF
Best Algebraic Geometry books
The writer, a number one determine in algebraic topology, presents a latest remedy of a protracted demonstrated set of questions during this very important examine region. The book's crucial objective--and major result--is the category theorem on k-variants and boundary invariants, which complement the classical photo of homology and homotopy teams, besides computations of sorts which are acquired by way of using this theorem.
In keeping with a path given to gifted high-school scholars at Ohio college in 1988, this booklet is largely a complicated undergraduate textbook in regards to the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really expert treatises on fractal geometry.
This quantity comprises the improved lectures given at a convention on quantity conception and mathematics geometry held at Boston collage. It introduces and explains the numerous principles and methods utilized by Wiles, and to give an explanation for how his consequence could be mixed with Ribets theorem and concepts of Frey and Serre to turn out Fermats final Theorem.
Extra info for Lectures on Hilbert Modular Varieties and Modular Forms (Crm Monograph Series)