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CATEGORIES:Number Theory Seminar
SUMMARY:Functoriality of the Canonical Fractional Galois I
deal - Victor Snaith
DTSTART;TZID=Europe/London:20080506T143000
DTEND;TZID=Europe/London:20080506T153000
UID:TALK11934AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/11934
DESCRIPTION:A famous conjecture in number theory is the\nStark
conjecture\, which concerns the leading term of t
he Taylor series for\nArtin L-functions at s=0. A
few years ago\, en route to giving a proof of the\
nCoates-Sinnott conjecture\, I constructed a canon
ical fractional ideal inside\nthe rational group-r
ing of a finite\, abelian Galois group of a number
field\nextension. It's role in life was to annihi
late algebraic K-groups of number\nrings\, in a wa
y which imitated and extended Stickelberger's famo
us theorem from\nthe 1890's.\nRecently\, in number
theory\, several people have been studying non-co
mmutative\nIwasawa theory. In this one makes an Iw
asawa algebra out of an infinite Galois\nextension
with such Galois groups as GLnZp.\nThis talk will
(i) describe the canonical (abelian) fractional G
alois ideal (ii)\nits naturality properties (iii)
how to make a canonical non-abelian fractional\nGa
lois ideal and (iv) it leads conjecturally to a tw
o-sided ideal in the\nIwasawa algebra.\nThis is jo
int work with Paul Buckingham.\n
LOCATION:MR13
CONTACT:Tim Dokchitser
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