A note on purity of crystalline local systems

TL;DR

This paper proves a purity result for crystalline local systems on smooth p-adic affine formal schemes using prismatic theory, advancing understanding of their structural properties.

Contribution

It introduces a new purity theorem for crystalline local systems leveraging prismatic descriptions, providing deeper insights into their structure.

Findings

Established a purity result for crystalline local systems.

Utilized prismatic theory to prove the main theorem.

Enhanced understanding of crystalline local systems in p-adic geometry.

Abstract

In this short note, we prove a purity result for crystalline local systems on a smooth $p$-adic affine formal scheme. Our method is based on the prismatic description of crystalline local systems.