A famous conjecture in number theory is the
Stark conjecture, which concerns the leading term of the Taylor series for
Artin L-functions at s=0. A few years ago, en route to giving a proof of the
Coates-Sinnott conjecture, I constructed a canonical fractional ideal inside
the rational group-ring of a finite, abelian Galois group of a number field
extension. It's role in life was to annihilate algebraic K-groups of number
rings, in a way which imitated and extended Stickelberger's famous theorem from
Recently, in number theory, several people have been studying non-commutative
Iwasawa theory. In this one makes an Iwasawa algebra out of an infinite Galois
extension with such Galois groups as GLn(Zp).
This talk will (i) describe the canonical (abelian) fractional Galois ideal (ii)
its naturality properties (iii) how to make a canonical non-abelian fractional
Galois ideal and (iv) it leads conjecturally to a two-sided ideal in the
This is joint work with Paul Buckingham.