New perspectives on $p$-adic regulator formulae

TL;DR

This paper extends the proof of the $p$-adic regulator formula for Asai--Flach classes to finite slope cases without finite polynomial cohomology, simplifying computations for diagonal classes using a pullback approach.

Contribution

It generalizes the $p$-adic regulator formula proof to finite slope cases and introduces a simplified method for diagonal classes based on recent pullback techniques.

Findings

Extended the $p$-adic regulator formula proof to finite slope cases.

Simplified computations for diagonal classes using a pullback construction.

Removed the need for finite polynomial cohomology in the proof.

Abstract

We generalise the proof of the $p$-adic regulator formula for Asai--Flach classes to the finite slope case, without using finite polynomial cohomology. Moreover, we simplify the analogous computation for diagonal classes, relying on a pullback construction inspired by recent work of Sangiovanni-Vincentelli--Skinner.