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University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Dimensions of Iwasawa algebras and their representations

## Dimensions of Iwasawa algebras and their representationsAdd to your list(s) Download to your calendar using vCal - James Timmins, University of Oxford
- Friday 28 January 2022, 15:00-16:00
- CMS MR15.
If you have a question about this talk, please contact Tom Adams. The Iwasawa algebra of a compact p-adic Lie group is fundamental to the study of the representations of the group. Understanding this representation theory is crucial in progress towards a (mod p)local Langlands correspondence. However, much remains unknown about Iwasawa algebras and their modules. In 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 – Krull dimension and canonical dimension – and survey previously known examples. Our main result is a new bound on these dimensions for the group SL_2(O_F), where F is a finite extension of the p-adic numbers. When F is a quadratic extension, we find the Krull dimension is exactly 5, as predicted by a conjecture of Ardakov and Brown. This talk is part of the Junior Algebra/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
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