Conjectures in Arithmetic Algebraic Geometry

Language: English

Published by Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Okt 2013, 2013

366309507X / 9783663095071

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This item is printed on demand - Print on Demand Titel. Neuware -In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math ematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce L functions, the main, motivation being the calculation of class numbers. In partic ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet 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 properties of L-functions. Twentieth century number theory, class field theory and algebraic geome try only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, 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 generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind.Vieweg+Teubner Verlag, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 256 pp. Englisch.

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Title
Conjectures in Arithmetic Algebraic Geometry
Author
Wilfred W. J. Hulsbergen
Publisher
Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Okt 2013
Publication year
2013
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
366309507X
ISBN 13
9783663095071
Edition
2nd Edition
Item weight
448 grams
Dimensions
244x170x15 mm

buchversandmimpf2000

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