Item Details
Foundations of Arithmetic Differential Geometry
Alexandru Buium
 Format
 Book
 Published
 Providence, Rhode Island : American Mathematical Society, [2017]
 Language
 English
 Series
 Mathematical Surveys and Monographs
 ISBN
 9781470436230, 147043623X
 Summary
 "The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is 'intrinsically curved'; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before."Page 4 of cover.
 Contents
 Introduction
 Algebraic background
 Classical differential geometry revisited
 Arithmetic differential geometry : generalities
 Arithmetic differential geometry : the case of GLn
 Curvature and Galois groups of Ehresmann connections
 Curvature of Chern connections
 Curvature of LeviCività connections
 Curvature of Lax connections
 Open problems.
 Description
 x, 344 pages ; 27 cm.
 Notes
 Includes bibliographical references (pages 339342) and index.
 Series Statement
 Mathematical surveys and monographs ; volume 222
 Mathematical surveys and monographs ; no. 222
 Technical Details

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LEADER 03316cam a2200457 i 4500001 u7211266003 SIRSI005 20170727160633.0008 161208s2017 riu b 001 0 enga 2016056302a 9781470436230 q (hardcover)a 147043623X q (hardcover)a (OCoLC)965754191a pcca DLC b eng e rda c DLC d OCLCF d OCLCQ d OCLCO d YDX d BTCTA d BUF d KSU d GZN d YDX d OCLCO d OBE d NRCa QA641 b .B774 2017a 516.3/6 2 23a 11E57 a 11F85 a 14G20 a 53C21 2 msca Buium, Alexandru, d 1955 e author.a Foundations of arithmetic differential geometry / c Alexandru Buium.a Providence, Rhode Island : b American Mathematical Society, c [2017]a x, 344 pages ; c 27 cm.a text b txt 2 rdacontenta unmediated b n 2 rdamediaa volume b nc 2 rdacarriera Mathematical surveys and monographs ; v volume 222a Includes bibliographical references (pages 339342) and index.a Introduction  Algebraic background  Classical differential geometry revisited  Arithmetic differential geometry : generalities  Arithmetic differential geometry : the case of GLn  Curvature and Galois groups of Ehresmann connections  Curvature of Chern connections  Curvature of LeviCività connections  Curvature of Lax connections  Open problems.a "The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is 'intrinsically curved'; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before."Page 4 of cover.a Geometry, Differential.a Geometry, Differential. 2 fast 0 (OCoLC)fst00940919a Number theory x Forms and linear algebraic groups x Classical groups. 2 msca Number theory x Discontinuous groups and automorphic forms x $p$adic theory, local fields. 2 msca Algebraic geometry x Arithmetic problems. Diophantine geometry x Local ground fields. 2 msca Differential geometry x Global differential geometry x Methods of Riemannian geometry, including PDE methods; curvature restrictions. 2 msca American Mathematical Society, e issuing body, e publisher.a Mathematical surveys and monographs ; v no. 222.a Z0 b VA@a 8a QA641 .B774 2017 w LC i X031815400 l STACKS m MATH t BOOK
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Math  Stacks  N/A  Available 
QA641 .B774 2017 