Wilfred W. J. Hulsbergen Conjectures in Arithmetic Algebraic Geometry 9783528064334

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Автор: Wilfred W. J. Hulsbergen
Название: Conjectures in Arithmetic Algebraic Geometry
ISBN: 9783528064334
Издательство: Springer
Классификация:

Геометрия

Алгебраическая геометрия

ISBN-10: 3528064331
Обложка/Формат: Paperback
Страницы: 240
Вес: 0.36 кг.
Дата издания: 01.01.1992
Серия: Aspects of Mathematics
Язык: German
Размер: 234 x 156 x 14
Основная тема: Mathematics
Подзаголовок: A Survey
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 Fermats 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 Fermats 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 Riemanns 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 theoristss view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlets 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 Dirichlets 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.

Conjectures in Arithmetic Algebraic Geometry, Wilfred W. J. Hulsbergen