Stark's conjectures on the behavior of $L$-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to Stark's conjectures. The remaining six contributions touch on some major themes currently under exploration in the area, such as non-abelian and $p$-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and Barry Mazur. The book is suitable for graduate students and researchers interested in number theory.Fitting ideals and some algebra 2.1. ... is finite), and the exponent minus denotes taking the minus eigenspace under complex conjugation which is denoted by j in this paper: PROPOSITION 2.1.1. ... A good choice is afforded by the theory of Fitting ideals which we now explain. ... So for instance with R = Z, the module M = Z/n 17 A ... x Z/n, Z has Fitting ideal n1 . . . . . n, Z and annihilator lcm(n1, ... , nr.)anbsp;...

Title | : | Stark's Conjectures |

Author | : | David Burns |

Publisher | : | American Mathematical Soc. - 2004 |

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