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Foundations of arithmetic differential geometry / (Record no. 424430)

MARC details
000 -LEADER
fixed length control field 02170cam a2200241 i 4500
001 - CONTROL NUMBER
control field 138305
003 - CONTROL NUMBER IDENTIFIER
control field ISI Library, Kolkata
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180502164617.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 161208s2017 riu b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470436230 (alk. paper)
040 ## - CATALOGING SOURCE
Original cataloging agency ISI Library
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 510MS
Edition number 23
Item number Am512
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Buium, Alexandru,
Relator term author
245 10 - TITLE STATEMENT
Title Foundations of arithmetic differential geometry /
Statement of responsibility, etc Alexandru Buium.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Providence :
Name of publisher, distributor, etc American Mathematical Society,
Date of publication, distribution, etc ©2017.
300 ## - PHYSICAL DESCRIPTION
Extent x, 344 pages ;
Dimensions 27 cm.
490 0# - SERIES STATEMENT
Series statement Mathematical surveys and monographs ;
Volume number/sequential designation v 222.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Introduction --<br/>1. Algebraic background --<br/>2. Classical differential geometry revisited --<br/>3. Arithmetic differential geometry : generalities --<br/>4. Arithmetic differential geometry : the case of GLn --<br/>5. Curvature and Galois groups of Ehresmann connections --<br/>6. Curvature of Chern connections --<br/>7. Curvature of Levi-Civitáa connections --<br/>8. Curvature of Lax connections --<br/>9. Open problems.
520 ## - SUMMARY, ETC.
Summary, etc 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Differential geometry.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type Books
Holdings
Lost status Not for loan Home library Current library Date acquired Source of acquisition Cost, normal purchase price Full call number Accession Number Koha item type
    ISI Library, Kolkata ISI Library, Kolkata 23/03/2018 279 7258.46 510MS Am512 138305 Books
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