The main part of the book is devoted to discrete dynamical systems. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. It is based on the lectures given by the author at. Advanced differential geometry textbook mathoverflow. All three can be found in cassels book on local fields edit mentioned by laurent berger in a comment. The aim of this book is to introduce and develop an. Before this book appeared, it was not easy for graduate students and researchers to study p adic differential equations and related topics because on needed to read a lot of original papers. This construction is analogous to the construction of. Lectures on padic differential equations bernard dwork springer. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. Over the last 50 years the theory of padic differential equations has grown into an active area of. As to differential geometry on infinite dimensional manifolds, i used to have.
Now one can easily access these areas via this book. An introduction by fernando gouvea, he gives an explanation of the padic expansion of a rational number which im pretty sure i understand this, but a bit later he talks about the padic absolute value, which from what i understand is the same as. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. However, formatting rules can vary widely between applications and fields of interest or study. Picardfuchs modules, rigid cohomology and padic hodge theory. Also before studying a book like husemollers fiber bundles. Padicnumbersanintroductionuniversitext download free. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. I tried to select only the works in book formats, real books that are mainly in pdf format, so many wellknown htmlbased mathematics web pages and online tutorials are left out. The extension is achieved by an alternative interpretation of the concept of closeness or absolute value. Kedlaya 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. The paper used in this book is acidfree and falls within the guidelines established. Nov, 2006 integration of oneforms on padic analytic spaces.
Introduction to p adic analytic number theory download. Dec 06, 2012 the goal of this book is to offer such an opportunity, by way of a visit to the p adic universe. The reader is led into the rich structure of the fields qp and cp in a beautiful balance between analytic and algebraic aspects. Click here if you prefer a categorized directory of mathematics books. May 22, 2003 such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. The last part of the book contains a discussion of the applications of padic di erential equations in arithmetic geometry. Next we will explore analogues of the various types of connections encountered in classical di erential geometry. Krasners theory had little influence on the later global higher dimensional developments described in this volume, but was valued and further developed by adic analysts doing the theory of adic differential equations, etc. Click download or read online button to get introduction to p adic analytic number theory book now.
Is there a book or a few books that gives the basic theory of the different types of manifolds and their geometries in an integrated manner. Definitions and weierstrass equations, the group law on an elliptic curve, heights and the mordellweil theorem, the curve, completion of the proof of mordellweil, examples of rank calculations, introduction to the padic numbers, motivation, formal groups, points of finite order, minimal. The title is a little misleading, this book is more about differential geometry than it is about algebraic geometry. Analysis on the field of padic numbers padic analysis. Padicnumbersanintroductionuniversitext download free pdf. For b book foundations of arithmetic differential geometry, ams 2017.
Lately padic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. Of course, this approach is not meant to replace more systematic expositions of padic analysis or geometry. Written by a leading expert in the subject, this book is both a textbook on a topic. Over the last century, padic numbers and padic analysis have come to playa. Arithmetic differential operators over the padic integers by claire c. Its main purpose is to introduce the reader to padic analytic geometry and to the theory of padic analytic functions and di. A first course in curves and surfaces preliminary version fall, 2015 theodore shifrin university of georgia dedicated to the memory of shiingshen chern, my adviser and friend c 2015 theodore shifrin no portion of this work may be reproduced in any form without written permission of the author, other than. Foundations of arithmetic differential geometry book, 2017. This book will therefore become a standard reference for professionals especially in p adic analysis, number theory and algebraic geometry and welcomed as a textbook for students. Over the last 50 years the theory of padic differential equations has grown.
This book is the first comprehensive study of the subject. Kedlayas book is the first fully comprehensive one on padic differential. Over the last century, p adic numbers and p adic analysis have come to playa central role in modern number theory. This note provides the explanation about the following topics. Download for offline reading, highlight, bookmark or take notes while you read lectures on padic lfunctions. Padic norm, valuation, and expansion physics forums. A padic differential equation is a differential equation in which the functions. Analitikus m odszerek a p enz ugyekben bevezet es az anal zisbe di erential geometry diszkr et optimaliz alas diszkr et matematikai feladatok geometria igazs agos elosztasok interakt v anal zis feladatgyujtem eny matematika bsc hallgatok sz am ara introductory course in analysis matematikai p enzugy mathematical analysisexercises 12. The first 200 pages or so seem like a strong introduction to differential geometry with the book becoming slowly more specialized after that. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. The usual meaning taken for padic analysis is the theory of padicvalued functions on spaces of interest.
Introduction to harmonic analysis on reductive p adic groups, by allan j. This text is suitable for an undergrad who has taken some analysis and topology. Padic methods in number theory and algebraic geometry. In the course of their undergraduate careers, most mathematics majors see little beyond standard mathematics.
To introduce our adelic concept let us consider, for each p. Before this book appeared, it was not easy for graduate students and researchers to study p adic differential equations and related topics because one needed to read a lot of original papers. I rementber that dwork was very upset that there was no mention of krasner in the introduction to the book bgr referred to by conrad in this volume, and. Alexandru buium the aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. Ralph, 9781107674141, available at book depository with free delivery worldwide. Padic geometry mathematical association of america. Foundations of arithmetic differential geometry 10. All three can be found in cassels book on local fields.
By the different types i primary mean ck real manifolds, complex manifolds, real analytic and nonarchimeadian padic. For example, a closed padic analytic oneform defined on a simplyconnected domain does not necessarily have a primitive in the class of analytic functions. Stanford libraries official online search tool for books, media, journals, databases, government documents and more. Arithmetic differential operators over the padic integers. How i learned to stop worrying and love fontaine this is the rough outline of a talk i recently gave at the berkeley student algebraic geometry seminar on the progression of ideas that might lead one to define the hodgetate decomposition. The list is updated on a daily basis, so, if you want to bookmark this page, use one of the. This particular conference, held in trento, italy in may 1989, was dedicated to the memory of philippe robba, his important contributions to p adic analysis and especially to the theory of p adic differential equations. Pages 453557 from volume 178 20, issue 2 by konstantin ardakov, simon wadsley. Hey guys, i wrote this when i began reading the book mentioned in the post while i was stuck at an airport, and it immediately made it click as to why p adics matter. This is a wellwritten introduction to the world of p adic numbers. Both the authors previous results on geometric properties of smooth padic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of nonarchimedean analytic geometry, number theory, and algebraic geometry.
Before this book appeared, it was not easy for graduate students and researchers to study padic differential equations and related topics because one needed to read a lot of original papers. Possibility of an elementary differential geometry course. Voisin hodge theory and complex algebraic geometry, i. Arithmetic differential equations american mathematical society. This site is like a library, use search box in the widget to get ebook that you want. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. Among the many differences between classical and padic objects, those related to differential equations occupy a special place. Download for offline reading, highlight, bookmark or take notes while you read integration of oneforms on padic analytic spaces. This book, the first comprehensive and unified introduction to the. Applications of p adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation. However, it does cover what one should know about differential geometry before studying algebraic geometry. The right book, of course, depends on your background. In mathematics, the padic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
Calculus on manifolds, michael spivak, mathematical methods of classical mechanics, v. Fundamental algebraic geometry mathematical surveys and monographs. P adic analysis compared with real, by svetlana katok is a very gentle introduction to p adic numbers. This is a continuation of 9, where it was shown that kequivalent complex projective manifolds have the same betti numbers by using the theory of padic integrals and delignes solution to the weil conjecture. Over the last century, padic numbers and padic analysis have come to playa central role in modern number theory. Will merry, differential geometry beautifully written notes with problems sheets. In particular, two p adic numbers are considered to be close. Dr schikhof shows how p adic and real analysis differ, providing a large number of exercises. Introduction to harmonic analysis on reductive padic groups, by allan j. Padic methods in number theory and algebraic geometry ebook. The aim of this textbook is to give an introduction to di erential geometry. This book provides an overview of the theory of padic and more general nonarchimedean dynamical systems. Free elliptic curves books download ebooks online textbooks. Arithmetic differential geometry department of mathematics.
A course in p adic analysis, by alain robert is a more terse and advanced book on the subject. Kedlayas book is the first fully comprehensive one on padic differential equations, taking into account important progress in the last 15 years. This is a revised version of the lecture notes for the course on p adic geometry given by p. In mathematics, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. I have had a course in number theory where i studied marcus and also a course in differential geometry. Foundations of arithmetic differential geometry book. Second this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in di erent branches of differential geometry. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers.
Differential geometry over general base fields and rings iecl. This particular conference, held in trento, italy in may 1989, was dedicated to the memory of philippe robba, his important contributions to padic analysis and especially to the theory of padic differential equations. In particular, two padic numbers are considered to be close. In mathematics, padic analysis is a branch of number theory that deals with the mathematical analysis of functions of padic numbers the theory of complexvalued numerical functions on the padic numbers is part of the theory of locally compact groups. The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. One source to learn about them is the second half of serres book lie algebras and lie groups, and another is peter schneiders recent book. Stein nonabelian minimal closed ideals of transitive lie algebras, by j.
Kedlayas book is the first fully comprehensive one on p adic differential equations, taking into account important progress in the last 15 years. This is a wellwritten introduction to the world of padic numbers. In this new geometry the ring of integers plays the role of a ring of functions on an. The usual meaning taken for p adic analysis is the theory of p adic valued functions on spaces of interest. I rementber that dwork was very upset that there was no mention of krasner in the introduction to the book bgr. The goal of this book is to offer such an opportunity, by way of a visit. Regularity theorems and applicati nonelliptic problems, by alexander nagel and e. Absolute values on fields, ostrowskis classification of absolute values on u, cauchy sequences and completion, inverse limits,properties of zp, the field of p adic numbers, padic expansions, hensels lemma, finite fields, profinite groups, affine varieties, morphisms and rational maps, quadratic forms, rational points on. In this new edition of the book, i have not changed the contents of these six chapters at all, as they have proved to be good building blocks for many other. Fractal geometry for images of continuous embeddings ofpadic numbers and solenoids into euclidean spaces.
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