Conjectures in Arithmetic Algebraic Geometry: A Survey (Aspects of Mathematics, 18)

Hulsbergen, Wilfred W. J.:

ISBN 10: 3528064331 / ISBN 13: 9783528064334

Edité par Braunschweig. Friedr. Vieweg & Sohn Verlagsgesellschaft mbH., 1992

A propos de cet article

252 S. Zust: Gutes Exemplar. Schneller Versand und persönlicher Service - jedes Buch händisch geprüft und beschrieben - aus unserem Familienbetrieb seit über 25 Jahren. Eine Rechnung mit ausgewiesener Mehrwertsteuer liegt jeder unserer Lieferungen bei. Wir versenden mit der deutschen Post. Sprache: Englisch Gewicht in Gramm: 488 Softcover reprint of the original 1st ed. 1992.

N° de réf. du vendeur 360412

Détails bibliographiques

• Titre: Conjectures in Arithmetic Algebraic Geometry: A Survey (Aspects of Mathematics, 18)
• Éditeur: Braunschweig. Friedr. Vieweg & Sohn Verlagsgesellschaft mbH.
• Date de parution: 1992
• Langue: anglais
• ISBN à 10 chiffres: 3528064331
• ISBN à 13 chiffres: 9783528064334
• Reliure: Karton Karton
• État de l'article: Sehr gut
• Poids: 488 grammes
• Catalogues du vendeur:
  • Mathematik

A propos de ce titre

Synopsis

In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro- duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich- let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper- ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza- tion of Dirichlet's L-functions with a generalization of class field the- ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.