The Resource Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)

Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)

Label
Topics in the Theory of Algebraic Function Fields
Title
Topics in the Theory of Algebraic Function Fields
Statement of responsibility
by Gabriel Daniel Villa Salvador
Creator
Author
Author
Subject
Language
  • eng
  • 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
Member of
http://library.link/vocab/creatorName
Villa Salvador, Gabriel Daniel
Dewey number
512.7
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
pM2SAg-q1Kk
Language note
English
LC call number
QA241-247.5
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Mathematics: Theory & Applications
http://library.link/vocab/subjectName
  • Number theory
  • Functions of complex variables
  • Geometry, algebraic
  • Field theory (Physics)
  • Global analysis (Mathematics)
  • Algebra
  • Number Theory
  • Functions of a Complex Variable
  • Algebraic Geometry
  • Field Theory and Polynomials
  • Analysis
  • Commutative Rings and Algebras
Label
Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (657 p.)
Form of item
online
Isbn
9780817645151
Media category
computer
Media type code
c
Other control number
10.1007/0-8176-4515-2
Specific material designation
remote
System control number
  • (CKB)1000000000492125
  • (EBL)3062231
  • (SSID)ssj0000320430
  • (PQKBManifestationID)11256854
  • (PQKBTitleCode)TC0000320430
  • (PQKBWorkID)10247806
  • (PQKB)10303432
  • (DE-He213)978-0-8176-4515-1
  • (MiAaPQ)EBC3062231
  • (EXLCZ)991000000000492125
Label
Topics in the Theory of Algebraic Function Fields, by Gabriel Daniel Villa Salvador, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (657 p.)
Form of item
online
Isbn
9780817645151
Media category
computer
Media type code
c
Other control number
10.1007/0-8176-4515-2
Specific material designation
remote
System control number
  • (CKB)1000000000492125
  • (EBL)3062231
  • (SSID)ssj0000320430
  • (PQKBManifestationID)11256854
  • (PQKBTitleCode)TC0000320430
  • (PQKBWorkID)10247806
  • (PQKB)10303432
  • (DE-He213)978-0-8176-4515-1
  • (MiAaPQ)EBC3062231
  • (EXLCZ)991000000000492125

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