Conjectures in Iwasawa Theory of Selmer groups and Iwasawa Algebras

Jishnu Ray (University of British Columbia)

23-Apr-2020, 21:00-22:00 (4 years ago)

Abstract: The Iwasawa Theory of Selmer groups provides a natural way for p-adic approach to the celebrated Birch and Swinnerton Dyer conjecture. Over a non-commutative p-adic Lie extension, the (dual) Selmer group becomes a module over a non-commutative Iwasawa algebra and its structure can be understood by analyzing “(left) reflexive ideals” in the Iwasawa algebra. In this talk, we will start by recalling several existing conjectures in Iwasawa Theory and then we will give an explicit ring-theoretic presentation, by generators and relations, of such Iwasawa algebras and sketch its implications in understanding the (two-sides) reflexive ideals. Generalizing Clozel’s work for SL(2), we will also show that such an explicit presentation of Iwasawa algebras can be obtained for a much wider class of p-adic Lie groups viz. uniform pro-p groups and the pro-p Iwahori of GL(n,Z_p). Further, if time permits, I will also sketch some of my recent Iwasawa theoretic results joint with Sujatha Ramdorai.

number theory

Audience: researchers in the topic

Comments: pretalk


UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.

Organizers: Kiran Kedlaya*, Alina Bucur, Aaron Pollack, Cristian Popescu, Claus Sorensen
*contact for this listing

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