Some lecture notes on padic hodge theory, from a course i taught with olivier brinon. For b book foundations of arithmetic differential geometry, ams 2017. Elements of padic differential geometry are described. Introduction to harmonic analysis on reductive p adic groups, by allan j. Picardfuchs modules, rigid cohomology and p adic hodge theory. Pages 453557 from volume 178 20, issue 2 by konstantin ardakov, simon wadsley. 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. Next we will explore analogues of the various types of connections encountered in classical di erential geometry. Elementary differential geometry by barrett oneill is another good book. Are you looking for how to get a copy of the pseudoreductive book with gabber and prasad. Notes on differential geometry part geometry of curves x. Springer made 10 year old graduate mathematics books free for. The last part of the book contains a discussion of the applications of padic di erential equations in arithmetic geometry.
Dec 06, 2012 the goal of this book is to offer such an opportunity, by way of a visit to the padic universe. Points q and r are equidistant from p along the curve. At a few points, we have expanded slightly on the material, in particular so as to provide a full construction of local shimura varieties and general moduli spaces of shtukas, along with some. This book stems from lectures given at the universities of t.
Differential geometry over general base fields and rings iecl. Voisin hodge theory and complex algebraic geometry, i. Work on these articles have been supported by the national science foundation since 1990, including the following grants. Important applications of padic numbers outside of algebra. I only read the first edition, but i thought it was written fairly well and did a good job of developing geometric intuition because of the number of pictures. The extension is achieved by an alternative interpretation of the concept of closeness or absolute value.
Also before studying a book like husemollers fiber bundles. This book, the first comprehensive and unified introduction to the. Springer have made a bunch of books available for free, here. Free differential geometry books download ebooks online. Download online ebook for pdf doc djvu readers padic function analysis lecture notes in pure and applied mathematics download online ebook for pdf doc djvu readers search this site.
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. This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. The paper used in this book is acidfree and falls within the guidelines established. Theory,henri cohen a course in differential geometry,wilhelm klingenberg. Of course, this approach is not meant to replace more systematic expositions of padic analysis or geometry. Local frames and curvature to proceed further, we need to more precisely characterize the local geometry of a curve in the neighborhood of some point. The reader is led into the rich structure of the fields qp and cp in a beautiful balance between analytic and algebraic aspects.
A padic differential equation is a differential equation, in which the functions involved. Perfectoid geometry doesnt transcend these previous attempts but. The last part of the book contains a discussion of the applications of p adic di erential equations in arithmetic geometry. The right book, of course, depends on your background. Now one can easily access these areas via this book.
Springer have made a bunch of maths books available for free, here. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. A course in padic analysis, by alain robert is a more terse and advanced book on the subject. Over the last 50 years the theory of padic differential equations has grown into an active area of. Padic analysis compared with real, by svetlana katok is a very gentle introduction to padic numbers. On medium, smart voices and original ideas take center stage with no ads in sight. The usual meaning taken for p adic analysis is the theory of p adic valued functions on spaces of interest. Introduction to differential geometry olivier biquard.
Introduction to p adic analytic number theory download. Stein nonabelian minimal closed ideals of transitive lie algebras, by j. This is a revised version of the lecture notes for the course on p adic geometry given by p. Brian conrad stanford mathematics stanford university. An introduction to padic analysis cambridge studies in advanced mathematics on free shipping on qualified orders. Arithmetic differential equations american mathematical society. Over the last century, p adic numbers and p adic analysis have come to playa central role in modern number theory. This text is suitable for an undergrad who has taken some analysis and topology. Differential geometry would leave many a physicist unaware that the book is. Padicnumbersanintroductionuniversitext download free pdf. Regularity theorems and applicati nonelliptic problems, by alexander nagel and e. 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. Polynomials and polynomial inequalities, peter borwein tamas erdelyi. We discuss recent developments in p adic geometry, ranging from foundational results such as the degeneration of the hodgetode rham spectral sequence for \compact p adic manifolds over new period maps on moduli spaces of abelian varieties to applications to the local and global langlands.
Some papers and preprints of chingli chai the more recent ones are preprints. 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. All the necessary properties of the curve can be derived algebraicly, as with the. Pdf some padic differential equations researchgate. What book a good introduction to differential geometry. Over the last century, padic numbers and padic analysis have come to playa. This is a wellwritten introduction to the world of padic numbers. This is a wellwritten introduction to the world of p adic numbers. Written by a leading expert in the subject, this book is both a textbook on a topic.
This book mostly focuses on classical differential geometry ie curves and surfaces in r3. Go to my differential geometry book work in progress home page. Arithmetic differential geometry department of mathematics. However, it does cover what one should know about differential geometry before studying algebraic geometry. Lectures on padic differential equations bernard dwork springer. This book is the second edition of anders kocks classical text, many notes have been included commenting on new developments.
A first course in curves and surfaces preliminary version summer, 2016 theodore shifrin university of georgia dedicated to the memory of shiingshen chern, my adviser and friend c 2016 theodore shifrin no portion of this work may be reproduced in any form without written permission of the author, other than. This site is like a library, use search box in the widget to get ebook that you want. 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. Its main purpose is to introduce the reader to padic analytic geometry and to the theory of padic analytic functions and di. Applied differential geometry a modern introduction vladimir g ivancevic defence science and technology organisation, australia tijana t ivancevic the university of adelaide, australia n e w j e r s e y l o n d o n s i n g a p o r e b e i j i n g s h a n g h a i h o n g k o n g ta i p e i c h e n n a i. Some differential geometry i once taught an introductory differential geometry course and was. Some papers and preprints of chingli chai penn math. 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 present work treats padic properties of solutions of the hypergeometric. Applications of p adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation. The title is a little misleading, this book is more about differential geometry than it is about algebraic geometry. Direct links to free springer maths books pdf versions.
This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Differential geometry of three dimensions download book. Picardfuchs modules, rigid cohomology and padic hodge theory. 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 text can be used as a manual for complex variable courses of various. Click download or read online button to get introduction to p adic analytic number theory book now. Do they have any important applications outside of algebra that i could easily ex.
Michael harris department of mathematics columbia university. 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. Ordinary differential equations, wolfgang walter p adic numbers, p adic analysis and zetafunctions partial differential equations, jeffrey rauch. Buy differential geometry on free shipping on qualified orders.