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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Dimensions of Iwasawa algebras and their represent
ations - James Timmins\, University of Oxford
DTSTART;TZID=Europe/London:20220128T150000
DTEND;TZID=Europe/London:20220128T160000
UID:TALK169319AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/169319
DESCRIPTION:The Iwasawa algebra of a compact p-adic Lie group
is fundamental to the study of the representations
of the group. Understanding this representation t
heory is crucial in progress towards a (mod p)loca
l Langlands correspondence. However\, much remains
unknown about Iwasawa algebras and their modules.
\n\nIn this talk we'll aim to measure the size of
the Iwasawa algebra and its representations. I'll
explain the algebraic tools we use to do this - Kr
ull dimension and canonical dimension - and survey
previously known examples. Our main result is a n
ew bound on these dimensions for the group SL_2(O_
F)\, where F is a finite extension of the p-adic n
umbers. When F is a quadratic extension\, we find
the Krull dimension is exactly 5\, as predicted by
a conjecture of Ardakov and Brown.\n
LOCATION:CMS MR15
CONTACT:Tom Adams
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