$B_{\mathrm{Sen}}$ via distributions on weight space

TL;DR

This paper establishes a canonical isomorphism between a ring of rigid-analytic distributions on p-adic weight space and Colmez's ring B_Sen, advancing the understanding of p-adic Hodge theory.

Contribution

It introduces a new ring of distributions on p-adic weight space and proves its isomorphism with B_Sen, providing a novel perspective in p-adic Hodge theory.

Findings

The ring of distributions is well-defined modulo torsion.

A canonical isomorphism with B_Sen is established.

The result bridges rigid-analytic distributions and p-adic Hodge structures.

Abstract

We introduce a certain ring of rigid-analytic distributions on $p$-adic weight space (modulo torsion) and show that it is canonically isomorphic to Colmez's ring $B_{\mathrm{Sen}}$.