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020 _a9780817645151
_99780817645151
024 7 _a10.1007/0817645152
_2doi
035 _avtls000333530
039 9 _a201509030722
_bVLOAD
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040 _aMX-SnUAN
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_cMX-SnUAN
_erda
050 4 _aQA241-247.5
100 1 _aVilla Salvador, Gabriel Daniel.
_eautor
_9305499
245 1 0 _aTopics in the Theory of Algebraic Function Fields /
_cby Gabriel Daniel Villa Salvador.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2006.
300 _axvI, 652 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aMathematics: Theory & Applications
500 _aSpringer eBooks
505 0 _aAlgebraic 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 _aThe 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.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780817644802
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/0-8176-4515-2
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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