### The Coates-Sinnott conjecture and eigenspaces of K-groups, by Pietro Cornacchia and Paul Arne Østvær

Let E signify a totally real Abelian number field with a prime power
conductor and ring of p-integers R_E for a prime p. Let G denote the Galois
group of E over the rationals, and let chi be a p-adic character of G of
order prime to p. The odd-primary results in this paper depend on the
Bloch-Kato conjecture, while the two-primary results are non-conjectural.
Theorem A calculates, under a minor restriction on chi, the Fitting ideals of
K_n(R_E;Z_p)(chi) over Z_p[G](chi). Here we require that n = 2 mod(4).
These Fitting ideals are principal, and generated by a Stickelberger element.
This gives a partial verification and also a strong indication of the
Coates-Sinnott conjecture. We also discuss (co)-descent for higher K-groups,
and prove in Theorem B a Hilbert Theorem 90 type of result for the transfer
map in higher K-theory of number fields.

Pietro Cornacchia <cornac@dm.unipi.it>

Paul Arne Østvær <paularne@math.uio.no>