A groundbreaking contribution to number theory that unifies classical and modern results
This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
Автор: Hida, Haruzo Название: P-adic automorphic forms on shimura varieties ISBN: 1441919236 ISBN-13(EAN): 9781441919236 Издательство: Springer Рейтинг: Цена: 23058.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Автор: Thomas Haines, Michael Harris Название: Shimura Varieties ISBN: 1108704867 ISBN-13(EAN): 9781108704861 Издательство: Cambridge Academ Рейтинг: Цена: 7603.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book is designed for graduate students and beginning researchers into the arithmetic theory of automorphic forms, and for all who want to know more about the Langlands program. It forms a sequel to On the Stabilization of the Trace Formula published in 2011.
Автор: Goro Shimura Название: Collected Papers I ISBN: 1493918095 ISBN-13(EAN): 9781493918096 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; 103 of Shimura`s most important papers are collected in four volumes.
Автор: Shimura Название: Collected Papers V ISBN: 3319325477 ISBN-13(EAN): 9783319325477 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement: 'To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.'
120 of Shimura's most important papers are collected in five volumes. Volume V contains his mathematical papers from 2002 onwards and some notes to the articles.
Автор: Goro Shimura Название: Collected Papers III ISBN: 1493918338 ISBN-13(EAN): 9781493918331 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement: "To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; 103 of Shimura`s most important papers are collected in four volumes.
Автор: Goro Shimura Название: Collected Papers II ISBN: 149391832X ISBN-13(EAN): 9781493918324 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement :" To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; 103 of Shimura`s most important papers are collected in four volumes.
Автор: Goro Shimura Название: Arithmetic of Quadratic Forms ISBN: 1461426189 ISBN-13(EAN): 9781461426189 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book examines algebraic number theory and the theory of semisimple algebras. It covers classification over an algebraic number field and classification over the ring of algebraic integers.
Автор: Goro Shimura Название: Collected Papers IV ISBN: 1493918370 ISBN-13(EAN): 9781493918379 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement: "To Goro Shimura for his important and extensive work on arithmetical geometry and automorphic forms; 103 of Shimura`s most important papers are collected in four volumes.
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.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru
