Representations of \(p\)-adic groups over commutative rings. (English) Zbl 07822680
Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 1. Prize lectures. Berlin: European Mathematical Society (EMS). 332-374 (2023).
Summary: Motivated by the Langlands program in representation theory, number theory, and geometry, the theory of representations of a reductive -adic group, originally in complex vector spaces, has been widely developed in modules over a commutative ring during the last two decades. This article surveys basic results obtained during this period, assuming some familiarity with the representation theory connected to the Langlands program. Addressed to a broader audience, the 2022 ICM Noether Lecture should be accessible without prerequisites and convey intuition on the most striking results.
For the entire collection see [Zbl 1532.00035].
For the entire collection see [Zbl 1532.00035].
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 20C08 | Hecke algebras and their representations |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
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