Back to Departmental Colloquium: Spring 2000
Departmental Colloquium
Date: Friday, Feb 18, 2000
Time: 4:15PM
Location: JWB 335
Cristian D. Popescu
University of Texas. Austin
Title |
Stark-type conjectures "over Z" |
Abstract |
In the 1970s and 1980s Stark developed a remarkable conjecture aimed at interpreting the first non-vanishing derivative of an Artin L -function $L_{K/k, S}(s,\chi)$ at s=0 in terms of the arithmetic properties of the Galois extension of global fields K/k. Work of Stark, Tate, and Chinburg has revealed far reaching applications of Stark’s Conjecture to Hilbert’s 12-th Problem and the theory of Galois module structure of groups of units and ideal-class groups. In his search for new examples of Euler systems, Rubin has formulated in 1994 a strong version (“over Z “, in Tate’s terminology) of Stark’s Conjecture for abelian L -functions of arbitrary order of vanishing at s=0}. Our recent study of the functorial base-change behavior of Rubin’s Conjecture led us to formulating a seemingly more natural Stark-type conjecture “over Z “. We will discuss and provide evidence for this new statement, as well as briefly describe the main goals of the conjectural program initiated by Stark. |
Number Theory
Commutative Algebra