The Resource Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador
Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador
Resource Information
The item Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 arithmeticalgebraic 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 geometricanalytic aspects of function fields, but leaves an indepth 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 RiemannRoch 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 RiemannHurwitz 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 14 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 59 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
 Language

 eng
 spa
 eng
 Extent
 1 online resource (xvi, 652 pages)
 Note
 Textbook for graduates
 Contents

 Algebraic and Numerical Antecedents
 Algebraic Function Fields of One Variable
 The RiemannRoch Theorem
 Examples
 Extensions and Galois Theory
 Congruence Function Fields
 The Riemann Hypothesis
 Constant and Separable Extensions
 The RiemannHurwitz Formula
 Cryptography and Function Fields
 to Class Field Theory
 Cyclotomic Function Fields
 Drinfeld Modules
 Automorphisms and Galois Theory
 Isbn
 9780817645151
 Label
 Topics in the theory of algebraic function fields
 Title
 Topics in the theory of algebraic function fields
 Statement of responsibility
 Gabriel Daniel Villa Salvador
 Language

 eng
 spa
 eng
 Summary
 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 arithmeticalgebraic 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 geometricanalytic aspects of function fields, but leaves an indepth 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 RiemannRoch 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 RiemannHurwitz 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 14 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 59 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
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Villa Salvador, Gabriel Daniel
 Dewey number
 515.9
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA341
 LC item number
 .V5513 2006eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Mathematics: Theory & Applications
 http://library.link/vocab/subjectName

 Algebraic functions
 Mathematics
 Functions
 Mathematics
 Functions
 Algebraic functions
 Algebraic functions
 Functions
 Mathematics
 Label
 Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador
 Note
 Textbook for graduates
 Bibliography note
 Includes bibliographical references (pages 639646) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Algebraic and Numerical Antecedents  Algebraic Function Fields of One Variable  The RiemannRoch Theorem  Examples  Extensions and Galois Theory  Congruence Function Fields  The Riemann Hypothesis  Constant and Separable Extensions  The RiemannHurwitz Formula  Cryptography and Function Fields  to Class Field Theory  Cyclotomic Function Fields  Drinfeld Modules  Automorphisms and Galois Theory
 Control code
 262687259
 Dimensions
 unknown
 Extent
 1 online resource (xvi, 652 pages)
 Form of item
 online
 Isbn
 9780817645151
 Lccn
 2006927769
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/0817645152.
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817644802
 Specific material designation
 remote
 System control number
 (OCoLC)262687259
 Label
 Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador
 Note
 Textbook for graduates
 Bibliography note
 Includes bibliographical references (pages 639646) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Algebraic and Numerical Antecedents  Algebraic Function Fields of One Variable  The RiemannRoch Theorem  Examples  Extensions and Galois Theory  Congruence Function Fields  The Riemann Hypothesis  Constant and Separable Extensions  The RiemannHurwitz Formula  Cryptography and Function Fields  to Class Field Theory  Cyclotomic Function Fields  Drinfeld Modules  Automorphisms and Galois Theory
 Control code
 262687259
 Dimensions
 unknown
 Extent
 1 online resource (xvi, 652 pages)
 Form of item
 online
 Isbn
 9780817645151
 Lccn
 2006927769
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/0817645152.
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9780817644802
 Specific material designation
 remote
 System control number
 (OCoLC)262687259
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