BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Generalising Stickelberger: Annihilators (and more) for class grou
 ps of number fields - David Solomon (King's College London)
DTSTART:20100525T133000Z
DTEND:20100525T143000Z
UID:TALK23498@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:Stickelberger's Theorem (from 1890) gives an explicit ideal in
  the Galois group-ring which annihilates the minus-part of the class group
  of a cyclotomic field. In the 1980s Tate and Brumer proposed a generalisa
 tion (the `Brumer-Stark conjecture') for any abelian extension of number f
 ields _K/k_\, with _K_ of CM type and _k_ totally real.\n\nBoth the theore
 m and the conjecture leave certain questions unanswered: Is the (generalis
 ed) Stickelberger ideal the full annihilator\, the Fitting ideal or what? 
 And\, at a more basic level\, what can we say in the plus part\, e.g. for 
 a real abelian field?  I shall discuss possible answers\, some still conje
 ctural\, to pieces of these puzzles\, using two new _p_-adic ideals of the
  group ring.
LOCATION:MR13
END:VEVENT
END:VCALENDAR