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...
Na minha lista:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado em: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Edição: | 1st ed. 2006. |
| Colecção: | Mathematics: theory & applications
|
| Assuntos: | |
| Acesso em linha: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
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 |
| LEADER | 04728nam a22004457a 4500 | ||
|---|---|---|---|
| 001 | 939494 | ||
| 008 | 080505q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN123717434 | ||
| 020 | |a 9780817645151 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.7 | ||
| 084 | |a 11-xx. 2000 | ||
| 084 | |a 12-xx. 2000 | ||
| 084 | |a 14-xx. 2000 | ||
| 100 | 1 | |a Villa Salvador, Gabriel Daniel, |d 19..- | |
| 245 | 1 | 0 | |a Topics in the theory of algebraic function fields |c Gabriel Daniel Villa Salvador. |
| 250 | |a 1st ed. 2006. | ||
| 260 | |a Boston, MA : |b Birkhäuser Boston. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Mathematics: theory & applications | |
| 500 | |a Description d'après consultation du 29 avril 2011 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a "Based on the original Spanish edition, Introducción a la teoría de las functiones algebraicas, fondo de cultura economica, Mexico, 2003" | ||
| 504 | |a Bibliogr. p. [639]-646. Index | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | |a Fonctions (mathématiques) | ||
| 650 | |a Fonctions algébriques | ||
| 650 | |a Théorie des champs (physique) | ||
| 765 | 0 | |t Introducción a la teoría de las functiones algebraicas | |
| 776 | 0 | |0 116375248 |t Topics in the theory of algebraic function fields |f Gabriel Daniel Villa Salvador |c Boston |n Birkhäuser |d 2006 |p 1 vol. (XVI-652 p.) |s Mathematics |z 0-8176-4480-6 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/0-8176-4515-2 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-JDX2DK4V-L |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747895384 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/0-8176-4515-2 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750908386 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/0-8176-4515-2 |z Accès INSA CVL | |
| 997 | |0 939494 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||