Foundations of arithmetic differential geometry / (Record no. 424430)
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000 -LEADER | |
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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 |
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 |