Relative K_0, annihilators, Fitting ideals and the Stickelberger phenomena, by Victor Snaith

When G is abelian and l is a prime we show how elements of the relative K-group K_0(Z_l[G], Q_l) give rise to annihilator/Fitting ideal relations of certain associated Z[G]-modules. Examples of this phenomenon are ubiquitous. Particularly, we give examples in which G is the Galois group of an extension of global fields and the resulting annihilator/Fitting ideal relation is closely connected to Stickelberger's Theorem and to the conjectures of Coates-Sinnott and Brumer.


Victor Snaith <vps@maths.soton.ac.uk>