P Adic Geometry
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P Adic Geometry
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Author : Matthew Baker
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
P Adic Geometry written by Matthew Baker 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 recent decades, p-adic geometry and p-adic cohomology theories have become indispensable tools in number theory, algebraic geometry, and the theory of automorphic representations. The Arizona Winter Schoo1 2007, on which the current book is based, was a unique opportunity to introduce graduate students to this subject." "Following invaluable introductions by John Tate and Vladimir Berkovich, two pioneers of non-archimedean geometry, Brian Conrad's chapter introduces the general theory of Tate's rigid analytic spaces, Raynaud's view of them as the generic fibers of formal schemes, and Berkovich spaces. Samit Dasgupta and Jeremy Teitelbaum discuss the p-adic upper half plane as an example of a rigid analytic space and give applications to number theory (modular forms and the p-adic Langlands program). Matthew Baker offers a detailed discussion of the Berkovich projective line and p-adic potential theory on that and more general Berkovich curves. Finally, Kiran Kedlaya discusses theoretical and computational aspects of p-adic cohomology and the zeta functions of varieties. This book will be a welcome addition to the library of any graduate student and researcher who is interested in learning about the techniques of p-adic geometry."--BOOK JACKET.
P Adic Numbers
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Author : Fernando Q. Gouvea
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
P Adic Numbers written by Fernando Q. Gouvea 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 2013-06-29 with Mathematics categories.
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.
P Adic Analysis And Mathematical Physics
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Author : Vasili? Sergeevich Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994
P Adic Analysis And Mathematical Physics written by Vasili? Sergeevich Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
Berkeley Lectures On P Adic Geometry
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Author : Peter Scholze
language : en
Publisher: Princeton University Press
Release Date : 2020-05-26
Berkeley Lectures On P Adic Geometry written by Peter Scholze 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 2020-05-26 with Mathematics categories.
Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
P Adic Numbers P Adic Analysis And Zeta Functions
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Author : Neal Koblitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
P Adic Numbers P Adic Analysis And Zeta Functions written by Neal Koblitz 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.
Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle. He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and GTM 97: "Introduction to Elliptic Curves and Modular Forms (Springer-Verlag).
A Course On Surgery Theory
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Author : Stanley Chang
language : en
Publisher: Princeton University Press
Release Date : 2021-01-26
A Course On Surgery Theory written by Stanley Chang 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 2021-01-26 with Mathematics categories.
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and respected series in science published, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. Book jacket.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Lectures On Formal And Rigid Geometry
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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2014-08-22
Lectures On Formal And Rigid Geometry written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
P Adic Differential Equations
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Author : Kiran S. Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10
P Adic Differential Equations written by Kiran S. Kedlaya 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 2010-06-10 with Mathematics categories.
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
Supersingular P Adic L Functions Maass Shimura Operators And Waldspurger Formulas
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Author : Daniel Kriz
language : en
Publisher: Princeton University Press
Release Date : 2021-11-09
Supersingular P Adic L Functions Maass Shimura Operators And Waldspurger Formulas written by Daniel Kriz 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 2021-11-09 with Mathematics categories.
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.