Duality and linearization for p-adic lie groups

TL;DR

This paper extends Lazard's Poincaré duality for p-adic Lie groups to include spectrum coefficients, focusing on the dualizing object expressed via the adjoint representation, thus advancing the understanding of duality in p-adic Lie theory.

Contribution

It generalizes Lazard's duality to spectrum coefficients and characterizes the dualizing object using linear data like the adjoint representation.

Findings

Duality is extended to spectrum coefficients.

The dualizing object is explicitly described via the adjoint representation.

Provides a new perspective on duality in p-adic Lie groups.

Abstract

We promote Lazard's Poincar\'e duality for p-adic Lie groups to spectrum coefficients. The key aspect is the determination of the dualizing object in terms of "linear" data, namely the adjoint representation.