STUDY ON SCHNEIDER-TEITELBAUM DUALITY FOR COMPACT p-ADIC LIE GROUP AND INTRODUCTION TO ITS MOD-p REDUCTION.

Author

Kasun Sandeepa Rathnayaka Rathnayaka Mudiyanselage, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2025

Degree Name

Master of Science

Department

Mathematics

First Advisor

Ban, Dubravka

Abstract

Let $K$ be finite extension of $\mathbb{Q}_{p}$, with the ring of integers $o_{K}$. This thesis investigates in detail about Schneider-Teitelbaum duality theory for compact $p$ -adic Lie group $\mathbf{G}_0$ including all necessary fundamental tools.This duality establishes a bijective correspondence between isomorphism classes of admissible $K$-Banach space representations of $\mathbf{G}_0$ and the isomorphism classes of simple $K[[\mathbf{G}_0]]$-modules. Based on this, we identify the mod-$p$ reduction on the $K$-Banach space side of the duality.