Number Theory Seminar

Tuesday 6 May 2008, MR13, 2:30pm

Functoriality of the Canonical Fractional Galois Ideal
Victor Snaith (Sheffield)


     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 the 1890's. 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 Iwasawa algebra.
    This is joint work with Paul Buckingham.

Last modified on 23/4/2008.

Comments/corrections to Tim Dokchitser