Cristian Popescu (UCSD)

TITLE: "On the Coates-Sinnott Conjectures"

ABSTRACT: The conjectures in the title were formulated in
the late 1970s as vast generalizations of the classical theorem of
Stickelberger. They make a subtle connection between the
**Z**[G(L/k)]-module structure of the Quillen
K-groups K_{*}(O_{L}) in an abelian extension L/k of
number fields and the values at negative integers of the
associated G(L/k)-equivariant L-functions Theta_{L/k}(s).

These conjectures are known to hold true if the base field k is
**Q**, due to work of Coates-Sinnott and Kurihara. In this
talk, we will provide evidence in support of these conjectures
over arbitrary totally real number fields k.