P Adic Automorphic Forms On Shimura Varieties
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P Adic Automorphic Forms On Shimura Varieties
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
P Adic Automorphic Forms On Shimura Varieties written by Haruzo Hida 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 2012-12-06 with Mathematics categories.
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.
Compactifications Of Pel Type Shimura Varieties And Kuga Families With Ordinary Loci
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Author : Kai-wen Lan
language : en
Publisher: #N/A
Release Date : 2017-07-21
Compactifications Of Pel Type Shimura Varieties And Kuga Families With Ordinary Loci written by Kai-wen Lan and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-21 with Mathematics categories.
This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families, and on the canonical and subcanonical extensions of automorphic bundles. The results in this book serve as the logical foundation of several recent developments in the theory of p-adic automorphic forms; and of the author's work with Harris, Taylor, and Thorne on the construction of Galois representations without any polarizability conditions, which is a major breakthrough in the Langlands program.This book is important for active researchers and graduate students who need to understand the above-mentioned recent works, and is written with such users of the theory in mind, providing plenty of explanations and background materials, which should be helpful for people working in similar areas. It also contains precise internal and external references, and an index of notation and terminologies. These are useful for readers to quickly locate materials they need.
Automorphic Forms Shimura Varieties And L Functions
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Author : Laurent Clozel
language : en
Publisher:
Release Date : 1990
Automorphic Forms Shimura Varieties And L Functions written by Laurent Clozel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Modular Forms And Special Cycles On Shimura Curves Am 161
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Author : Stephen S. Kudla
language : en
Publisher: Princeton University Press
Release Date : 2006-04-24
Modular Forms And Special Cycles On Shimura Curves Am 161 written by Stephen S. Kudla 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 2006-04-24 with Mathematics categories.
Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.
Topological Automorphic Forms
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Author : Mark Behrens
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-02-22
Topological Automorphic Forms written by Mark Behrens 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 2010-02-22 with Mathematics categories.
The authors apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type $U(1,n-1)$. These cohomology theories of topological automorphic forms ($\mathit{TAF}$) are related to Shimura varieties in the same way that $\mathit{TMF}$ is related to the moduli space of elliptic curves.
Automorphic Forms Shimura Varieties And L Functions
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Author : Laurent Clozel
language : en
Publisher:
Release Date : 1990
Automorphic Forms Shimura Varieties And L Functions written by Laurent Clozel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Elliptic Curves And Arithmetic Invariants
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves And Arithmetic Invariants written by Haruzo Hida 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 2013-06-13 with Mathematics categories.
This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.
Shimura Varieties
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Author : Thomas Haines
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-20
Shimura Varieties written by Thomas Haines 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 2020-02-20 with Mathematics categories.
This volume forms the sequel to "On the stabilization of the trace formula", published by International Press of Boston, Inc., 2011
Automorphic Forms And Galois Representations Volume 2
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Author : Fred Diamond
language : en
Publisher: Cambridge University Press
Release Date : 2014-10-16
Automorphic Forms And Galois Representations Volume 2 written by Fred Diamond 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 2014-10-16 with Mathematics categories.
Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.
Families Of Automorphic Forms And The Trace Formula
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Author : Werner Müller
language : en
Publisher: Springer
Release Date : 2016-09-20
Families Of Automorphic Forms And The Trace Formula written by Werner Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-20 with Mathematics categories.
Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
