Topics in the theory of algebraic function fields
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...
Enregistré dans:
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| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Udgivelse: | 1st ed. 2006. |
| Serier: | Mathematics: theory & applications
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| Fag: | |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Description d'après consultation du 29 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) "Based on the original Spanish edition, Introducción a la teoría de las functiones algebraicas, fondo de cultura economica, Mexico, 2003" |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Topics in the theory of algebraic function fields, Gabriel Daniel Villa Salvador, Boston, Birkhäuser, 2006, 1 vol. (XVI-652 p.), Mathematics, 0-8176-4480-6 |
| 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. |
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| Emne beskrivelse: | Description d'après consultation du 29 avril 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) "Based on the original Spanish edition, Introducción a la teoría de las functiones algebraicas, fondo de cultura economica, Mexico, 2003" |
| Bibliografi: | Bibliogr. p. [639]-646. Index |
| ISBN: | 9780817645151 |
| Adgang: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |