A famous conjecture in number theory is the
Stark conjecture, which concerns the leading term of the Taylor series for
Artin Lfunctions at s=0. A few years ago, en route to giving a proof of the
CoatesSinnott conjecture, I constructed a canonical fractional ideal inside
the rational groupring of a finite, abelian Galois group of a number field
extension. It's role in life was to annihilate algebraic Kgroups of number
rings, in a way which imitated and extended Stickelberger's famous theorem from
the 1890's.
Recently, in number theory, several people have been studying noncommutative
Iwasawa theory. In this one makes an Iwasawa algebra out of an infinite Galois
extension with such Galois groups as GL_{n}(Z_{p}).
This talk will (i) describe the canonical (abelian) fractional Galois ideal (ii)
its naturality properties (iii) how to make a canonical nonabelian fractional
Galois ideal and (iv) it leads conjecturally to a twosided ideal in the
Iwasawa algebra.
This is joint work with Paul Buckingham.
