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 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
- 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 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
- 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 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
- 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 639-646) 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 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
- 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
- 10.1007/0-8176-4515-2.
- Other physical details
- illustrations.
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-0-8176-4480-2
- 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 639-646) 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 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
- 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
- 10.1007/0-8176-4515-2.
- Other physical details
- illustrations.
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-0-8176-4480-2
- Specific material designation
- remote
- System control number
- (OCoLC)262687259
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Topics-in-the-theory-of-algebraic-function/MUumPOjRl_I/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Topics-in-the-theory-of-algebraic-function/MUumPOjRl_I/">Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
