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SUMMARY:Dimensions of Iwasawa algebras and their representations - James T
 immins\, University of Oxford
DTSTART:20220128T150000Z
DTEND:20220128T160000Z
UID:TALK167158@talks.cam.ac.uk
CONTACT:Tom Adams
DESCRIPTION:The Iwasawa algebra of a compact p-adic Lie group is fundament
 al to the study of the representations of the group. Understanding this re
 presentation theory is crucial in progress towards a (mod p)local Langland
 s correspondence. However\, much remains unknown about Iwasawa algebras an
 d their modules.\n\nIn this talk we'll aim to measure the size of the Iwas
 awa algebra and its representations. I'll explain the algebraic tools we u
 se to do this - Krull dimension and canonical dimension - and survey previ
 ously known examples. Our main result is a new bound on these dimensions f
 or the group SL_2(O_F)\, where F is a finite extension of the p-adic numbe
 rs. When F is a quadratic extension\, we find the Krull dimension is exact
 ly 5\, as predicted by a conjecture of Ardakov and Brown.\n
LOCATION:CMS MR11
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