Compactification Of Siegel Moduli Schemes

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Compactification Of Siegel Moduli Schemes

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Author : Ching-Li Chai
language : en
Publisher: Cambridge University Press
Release Date : 1985-12-12

Compactification Of Siegel Moduli Schemes written by Ching-Li Chai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-12 with Mathematics categories.

The main result of this monograph is to prove the existence of the toroidal compactification over Z(1/2).

Compactification Of Siegel Moduli Schemes

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Author : Ching-Li Chai
language : en
Publisher: Cambridge University Press
Release Date : 1985-12-12

Compactification Of Siegel Moduli Schemes written by Ching-Li Chai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-12 with Mathematics categories.

The Siegel moduli scheme classifies principally polarised abelian varieties and its compactification is an important result in arithmetic algebraic geometry. The main result of this monograph is to prove the existence of the toroidal compactification over Z (1/2). This result should have further applications and is presented here with sufficient background material to make the book suitable for seminar courses in algebraic geometry, algebraic number theory or automorphic forms.

Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms

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Author : Kazuyuki Hatada
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms written by Kazuyuki Hatada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.

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Smooth Compactifications Of Locally Symmetric Varieties

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Author : Avner Ash
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-14

Smooth Compactifications Of Locally Symmetric Varieties written by Avner Ash and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.

The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal method for the resolution of a class of singularities in algebraic geometry.

Geometric Invariant Theory

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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-03-29

Geometric Invariant Theory written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-29 with Mathematics categories.

This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.

Arithmetic Compactifications Of Pel Type Shimura Varieties

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Author : Kai-Wen Lan
language : en
Publisher: Princeton University Press
Release Date : 2013-03-24

Arithmetic Compactifications Of Pel Type Shimura Varieties written by Kai-Wen Lan and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-24 with Mathematics categories.

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary. This book explains in detail the following topics about PEL-type Shimura varieties and their compactifications: A construction of smooth integral models of PEL-type Shimura varieties by defining and representing moduli problems of abelian schemes with PEL structures An analysis of the degeneration of abelian varieties with PEL structures into semiabelian schemes, over noetherian normal complete adic base rings A construction of toroidal and minimal compactifications of smooth integral models of PEL-type Shimura varieties, with detailed descriptions of their structure near the boundary Through these topics, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai).

Hilbert Modular Forms And Iwasawa Theory

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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15

Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.

Commutator Theory For Congruence Modular Varieties

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Author : Ralph Freese
language : en
Publisher: CUP Archive
Release Date : 1987-08-20

Commutator Theory For Congruence Modular Varieties written by Ralph Freese and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-08-20 with Mathematics categories.

Semigroup Theory And Its Applications

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Author : Alfred Hoblitzelle Clifford
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-16

Semigroup Theory And Its Applications written by Alfred Hoblitzelle Clifford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-16 with Mathematics categories.

This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.

Arithmetic Groups And Their Generalizations

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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Arithmetic Groups And Their Generalizations written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.