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2000, ISBN: 9780387207117
ID: 9780387207117
This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry:1. An elementary construction of Shimura varieties as moduli of abelian schemes.2. p-adic deformation theory of automorphic forms on Shimura varieties.3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry:1. An elementary construction of Shimura varieties as moduli of abelian schemes.2. p-adic deformation theory of automorphic forms on Shimura varieties.3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others).Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000). Textbooks New, Books~~Mathematics~~Geometry~~Algebraic, p-Adic-Automorphic-Forms-on-Shimura-Varieties~~Haruzo-Hida, 999999999, p-Adic Automorphic Forms on Shimura Varieties, Haruzo Hida, 0387207112, Springer New York, , , , , Springer New York
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MPN: , SKU 9780387207117 Frais d'envoiplus shipping costs, Livraison non-comprise
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2000, ISBN: 9780387207117
ID: 5931607
In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon- ical p-adic counterpart of several variables. I immediately decided to find out the reason. In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon- ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de- pending on their weights, and this book is the outgrowth of the lectures given there. Books, Science and Geography~~Mathematics~~Number Theory, P-Adic Automorphic Forms On Shimura Varieties~~Book~~9780387207117~~Haruzo Hida, , , , , , , , , ,, [PU: Springer]
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MPN: , SKU 5931607 Frais d'envoizzgl. Versandkosten, Livraison non-comprise
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2000
ISBN: 9780387207117
ID: 978038720711
This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry:1. An elementary construction of Shimura varieties as moduli of abelian schemes2. p-adic deformation theory of automorphic forms on Shimura varieties3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura varietyThe book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat''s Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others).Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000). Haruzo Hida, Books, Science and Nature, P-adic Automorphic Forms On Shimura Varieties Books>Science and Nature, Springer New York
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2000, ISBN: 9780387207117
ID: a879bf6e7bc0ad84a62804616700fee3
P-Adic Automorphic Forms on Shimura Varieties This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry:1. An elementary construction of Shimura varieties as moduli of abelian schemes2. p-adic deformation theory of automorphic forms on Shimura varieties3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura varietyThe book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others).Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000). Bücher / Fremdsprachige Bücher / Englische Bücher 978-0-387-20711-7, Springer Verlag GmbH
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2000, ISBN: 9780387207117
ID: 81477927
This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry:1. An elementary construction of Shimura varieties as moduli of abelian schemes2. p-adic deformation theory of automorphic forms on Shimura varieties3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura varietyThe book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat´s Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others).Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000). P-Adic Automorphic Forms on Shimura Varieties Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer Verlag GmbH
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Titre: | P-Adic Automorphic Forms on Shimura Varieties |
ISBN: | 9780387207117 |
Informations détaillées sur le livre - P-Adic Automorphic Forms on Shimura Varieties
EAN (ISBN-13): 9780387207117
ISBN (ISBN-10): 0387207112
Version reliée
Date de parution: 2004
Editeur: Springer-Verlag GmbH
390 Pages
Poids: 0,689 kg
Langue: eng/Englisch
Livre dans la base de données depuis 04.06.2007 20:05:21
Livre trouvé récemment le 06.02.2016 21:23:59
ISBN/EAN: 9780387207117
ISBN - Autres types d'écriture:
0-387-20711-2, 978-0-387-20711-7
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