Lie Groups Smooth Compactification Of Locally Symmetric Varieties
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Lie Groups Smooth Compactification Of Locally Symmetric Varieties
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Author : Sophus Lie
language : de
Publisher:
Release Date : 1975
Lie Groups Smooth Compactification Of Locally Symmetric Varieties written by Sophus Lie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Lie groups categories.
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.
Lie Groups
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Author : Nolan Wallach
language : en
Publisher:
Release Date : 1975
Lie Groups written by Nolan Wallach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Lie Groups
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Author : Daniel Bump
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-01
Lie Groups written by Daniel Bump 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 2013-10-01 with Mathematics categories.
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
Groups Generators Syzygies And Orbits In Invariant Theory
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Author : V. L. Popov
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-05
Groups Generators Syzygies And Orbits In Invariant Theory written by V. L. Popov 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 2011-01-05 with Mathematics categories.
The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type
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Author : Fritz Hörmann
language : en
Publisher: American Mathematical Society
Release Date : 2014-11-05
The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type written by Fritz Hörmann and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-05 with Mathematics categories.
This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.
Galois Representations In Arithmetic Algebraic Geometry
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Author : A. J. Scholl
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-26
Galois Representations In Arithmetic Algebraic Geometry written by A. J. Scholl 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 1998-11-26 with Mathematics categories.
Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.
Compactifications Of Symmetric And Locally Symmetric Spaces
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Author : Armand Borel
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
Compactifications Of Symmetric And Locally Symmetric Spaces written by Armand Borel 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 2005-12-08 with Mathematics categories.
Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology
Selected Papers On Number Theory And Algebraic Geometry
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Author : Katsumi Nomizu
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Selected Papers On Number Theory And Algebraic Geometry written by Katsumi Nomizu 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 1996 with Mathematics categories.
This book presents papers that originally appeared in the Japanese journal Sugaku from the Mathematical Society of Japan. The papers explore the relationship between number theory and algebraic geometry.
Arithmetic Compactifications Of Pel Type Shimura Varieties
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Author : Kai-Wen Lan
language : en
Publisher: Princeton University Press
Release Date : 2013-03-21
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 2013-03-21 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).