On derivatives of Artin L-series

We present a universal theory of refined Stark conjectures. We give evidence in support of these explicit and very general conjectures, including a full proof in several important cases, and explain the connection to previous conjectures of Bloch and Kato, of Lichtenbaum and of Serre and Tate. We also deduce a wide range of unconditional consequences of these results concerning the annihilation, as Galois modules, of ideal class groups by explicit elements constructed from the values of higher order derivatives of (non-abelian) Artin L-series.