Full faithfulness theorem for torsion crystalline representations

TL;DR

This paper extends Kisin's full faithfulness theorem from crystalline p-adic representations to their torsion counterparts, establishing a key property in p-adic Hodge theory.

Contribution

It proves the torsion analogue of Kisin's theorem, a significant advancement in understanding torsion crystalline representations.

Findings

Established full faithfulness for torsion crystalline representations

Extended Kisin's theorem to a broader class of representations

Provided new tools for p-adic Hodge theory analysis

Abstract

Mark Kisin proved that a certain restriction functor on crystalline p-adic representations is fully faithful. In this paper, we prove the torsion analogue of Kisin's theorem.