MARC details
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04098nam a22005415i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-8176-4515-1 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20251006084435.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2006 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780817645151 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
99780817645151 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/0-8176-4515-2 |
| Source of number or code |
doi |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.7 |
| Edition information |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Villa Salvador, Gabriel Daniel. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Topics in the Theory of Algebraic Function Fields |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Gabriel Daniel Villa Salvador. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Boston, MA : |
| Name of producer, publisher, distributor, manufacturer |
Birkhäuser Boston, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2006. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XVI, 652 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Mathematics: Theory & Applications |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Algebraic and Numerical Antecedents -- Algebraic Function Fields of One Variable -- The Riemann-Roch Theorem -- Examples -- Extensions and Galois Theory -- Congruence Function Fields -- The Riemann Hypothesis -- Constant and Separable Extensions -- The Riemann-Hurwitz Formula -- Cryptography and Function Fields -- to Class Field Theory -- Cyclotomic Function Fields -- Drinfeld Modules -- Automorphisms and Galois Theory. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometric-analytic aspects of function fields, but leaves an in-depth examination from this perspective to others. Key topics and features: * Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces * Focuses on the Riemann-Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more * Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemann-Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules * Explains both the similarities and fundamental differences between function fields and number fields * Includes many exercises and examples to enhance understanding and motivate further study The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICS. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
GEOMETRY, ALGEBRAIC. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
ALGEBRA. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
FIELD THEORY (PHYSICS). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
GLOBAL ANALYSIS (MATHEMATICS). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
FUNCTIONS OF COMPLEX VARIABLES. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
NUMBER THEORY. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICS. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
NUMBER THEORY. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
FUNCTIONS OF A COMPLEX VARIABLE. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
ALGEBRAIC GEOMETRY. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
FIELD THEORY AND POLYNOMIALS. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
ANALYSIS. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
COMMUTATIVE RINGS AND ALGEBRAS. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Relationship information |
Printed edition: |
| International Standard Book Number |
9780817644802 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Mathematics: Theory & Applications |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/0-8176-4515-2">http://dx.doi.org/10.1007/0-8176-4515-2</a> |
| Public note |
Ver el texto completo en las instalaciones del CICY |
| 912 ## - |
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| -- |
ZDB-2-SMA |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Libros electrónicos |
