Free Download Conjectures in Arithmetic Algebraic Geometry: A Survey by Wilfred W. J. Hulsbergen

English | PDF | 1992 | 246 Pages | ISBN : 3528064331 | 11.1 MB

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.