Torsion graded pieces of Nyggard filtration for crystalline representation

Tong Liu

paper

Torsion graded pieces of Nyggard filtration for crystalline representation

arXiv:2408.13422

Abstract

Let $K$ be a unramified $p$ -adic field with the absolute Galois group $G_{K}$ and $T$ a crystalline $Z_{p}$ -representation of $G_{K}$ . We study the graded pieces of integral filtration on $D_{dR} (T)$ given by Nyggard filtration of the attached Breuil-Kisin module of $T$ . We show that the $i$ -graded piece has nontrivial $p$ -torsion only if $i = r_{j} + m p$ for a Hodge-Tate weight $r_{j}$ of $T$ and $m$ a positive integer.

10 pages