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SUMMARY:Functoriality of the Canonical Fractional Galois Ideal - Victor Sn
 aith
DTSTART:20080506T133000Z
DTEND:20080506T143000Z
UID:TALK11934@talks.cam.ac.uk
CONTACT:Tim Dokchitser
DESCRIPTION:A famous conjecture in number theory is the\nStark conjecture\
 , which concerns the leading term of the Taylor series for\nArtin L-functi
 ons at s=0. A few years ago\, en route to giving a proof of the\nCoates-Si
 nnott conjecture\, I constructed a canonical fractional ideal inside\nthe 
 rational group-ring of a finite\, abelian Galois group of a number field\n
 extension. It's role in life was to annihilate algebraic K-groups of numbe
 r\nrings\, in a way which imitated and extended Stickelberger's famous the
 orem from\nthe 1890's.\nRecently\, in number theory\, several people have 
 been studying non-commutative\nIwasawa theory. In this one makes an Iwasaw
 a algebra out of an infinite Galois\nextension with such Galois groups as 
 GLnZp.\nThis talk will (i) describe the canonical (abelian) fractional Gal
 ois ideal (ii)\nits naturality properties (iii) how to make a canonical no
 n-abelian fractional\nGalois ideal and (iv) it leads conjecturally to a tw
 o-sided ideal in the\nIwasawa algebra.\nThis is joint work with Paul Bucki
 ngham.\n
LOCATION:MR13
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