the conjectures in the title were formulated in the late 1970s as vast generalizations of the classical theorem of stickelberger. they make a very subtle connection between the $\bbb z[g(f/k)]$--module structure of the quillen k-groups k${_\ast}(o_f)$ in an abelian extension $f/k$ of number fields and the values at negative integers of the associated $g(f/k)$--equivariant $l$--functions $\theta_{f/k}(s)$. these conjectures are known to hold true if the base field $k$ is $\bbb q$, 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 $k$.