Download Arithmetic Compactifications of PEL-Type Shimura Varieties by Kai-Wen Lan PDF

By Kai-Wen Lan

By learning the degeneration of abelian forms with PEL buildings, this booklet explains the compactifications of delicate quintessential types of all PEL-type Shimura kinds, delivering the logical starting place for numerous interesting contemporary advancements. The ebook is designed to be available to graduate scholars who've an knowing of schemes and abelian varieties.

PEL-type Shimura forms, that are average generalizations of modular curves, are helpful for learning the mathematics homes of automorphic kinds and automorphic representations, and so they have performed vital roles within the improvement of the Langlands software. As with modular curves, it's fascinating to have vital versions of compactifications of PEL-type Shimura forms that may be defined in adequate aspect close to the boundary. This e-book explains intimately the subsequent subject matters approximately PEL-type Shimura kinds and their compactifications:

  • A building of gentle indispensable versions of PEL-type Shimura types via defining and representing moduli difficulties of abelian schemes with PEL constructions
  • An research of the degeneration of abelian types with PEL constructions into semiabelian schemes, over noetherian basic entire adic base earrings
  • A building of toroidal and minimum compactifications of delicate critical versions of PEL-type Shimura types, with special descriptions in their constitution close to the boundary

Through those issues, the publication generalizes the speculation of degenerations of polarized abelian forms and the appliance of that concept to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as built via Mumford, Faltings, and Chai).

Show description

Read or Download Arithmetic Compactifications of PEL-Type Shimura Varieties (London Mathematical Society Monographs) PDF

Best geometry & topology books

Hyperbolic Geometry (Springer Undergraduate Mathematics Series)

The geometry of the hyperbolic airplane has been an energetic and interesting box of mathematical inquiry for many of the previous centuries. This publication offers a self-contained creation to the topic, offering the reader with a company snatch of the strategies and methods of this gorgeous sector of arithmetic.

Fractal Solutions for Understanding Complex Systems in Earth Sciences (Springer Earth System Sciences)

This booklet bargains with fractals in realizing difficulties encountered in earth technological know-how, and their suggestions. It begins with an research of 2 sessions of equipment (homogeneous fractals random types, and homogeneous resource distributions or “one element” distributions) generally subtle within the geophysical group, in particular for learning capability fields and their comparable resource distributions.

Differential Forms and Connections

This 1994 e-book introduces the instruments of contemporary differential geometry, external calculus, manifolds, vector bundles and connections, to complicated undergraduate and starting graduate scholars in arithmetic, physics and engineering. The ebook covers either classical floor conception and the trendy concept of connections and curvature, and encompasses a bankruptcy on purposes to theoretical physics.

Euclidean and Non-Euclidean Geometry: An Analytic Approach

This e-book provides a rigorous therapy of the basics of aircraft geometry: Euclidean, round, elliptical and hyperbolic. the first function is to acquaint the reader with the classical result of aircraft Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, class of isometries, attitude addition and trigonometrical formulae.

Extra info for Arithmetic Compactifications of PEL-Type Shimura Varieties (London Mathematical Society Monographs)

Example text

Download PDF sample

Rated 4.24 of 5 – based on 14 votes