Cristian Popescu (UCSD) <BR><BR>

TITLE: "On the Coates-Sinnott Conjectures" <BR><BR>


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
<b>Z</b>[G(L/k)]-module structure of the Quillen 
K-groups K<sub>*</sub>(O<sub>L</sub>) 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<sub>L/k</sub>(s).
<BR><BR>

These conjectures are known to hold true if the base field k is
<b>Q</b>, 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.