Cargando…
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston, MA :
Birkhäuser Boston : Imprint: Birkhäuser,
2006.
|
| Edición: | 1st ed. 2006. |
| Colección: | Mathematics: Theory & Applications
|
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-0-8176-4515-1 | ||
| 003 | DE-He213 | ||
| 005 | 20220126113503.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 100301s2006 xxu| s |||| 0|eng d | ||
| 020 | |a 9780817645151 |9 978-0-8176-4515-1 | ||
| 024 | 7 | |a 10.1007/0-8176-4515-2 |2 doi | |
| 050 | 4 | |a QA241-247.5 | |
| 072 | 7 | |a PBH |2 bicssc | |
| 072 | 7 | |a MAT022000 |2 bisacsh | |
| 072 | 7 | |a PBH |2 thema | |
| 082 | 0 | 4 | |a 512.7 |2 23 |
| 100 | 1 | |a Villa Salvador, Gabriel Daniel. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Topics in the Theory of Algebraic Function Fields |h [electronic resource] / |c by Gabriel Daniel Villa Salvador. |
| 250 | |a 1st ed. 2006. | ||
| 264 | 1 | |a Boston, MA : |b Birkhäuser Boston : |b Imprint: Birkhäuser, |c 2006. | |
| 300 | |a XVI, 652 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Mathematics: Theory & Applications | |
| 505 | 0 | |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. | |
| 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 | 0 | |a Number theory. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 0 | |a Algebraic fields. | |
| 650 | 0 | |a Polynomials. | |
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Commutative algebra. | |
| 650 | 0 | |a Commutative rings. | |
| 650 | 1 | 4 | |a Number Theory. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 650 | 2 | 4 | |a Field Theory and Polynomials. |
| 650 | 2 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Commutative Rings and Algebras. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9780817671198 |
| 776 | 0 | 8 | |i Printed edition: |z 9780817644802 |
| 830 | 0 | |a Mathematics: Theory & Applications | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/0-8176-4515-2 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||