A note on crystalline liftings in the ${\mathbb{Q}}_p$ case

Abstract

Let $p>2$ be a prime. Let $\rho$ be a crystalline representation of $G_{{\mathbb{Q}}_p}$ with distinct Hodge-Tate weights in $[0,p]$, such that its reduction $\overline{\rho }$ is upper triangular. Under certain conditions, we prove that $\overline{\rho }$ has an upper triangular crystalline lift ${\rho }^{\prime }$ such that $\mathrm{HT}({\rho }^{\prime })=\mathrm{HT}(\rho )$. The method is based on the author's previous work, combined with an inspiration from the work of Breuil-Herzig.

Final version. arXiv admin note: text overlap with arXiv:1504.01233

References in corpus (1)

• G-valued crystalline representations with minuscule p-adic Hodge type