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Limit of torsion semistable Galois representations with unbounded weights


Author: Hui Gao
Journal: Proc. Amer. Math. Soc. 146 (2018), 3275-3283
MSC (2010): Primary 11F80, 11F33
DOI: https://doi.org/10.1090/proc/14044
Published electronically: March 30, 2018
MathSciNet review: 3803654
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Abstract: Let $K$ be a complete discrete valuation field of characteristic $(0, p)$ with perfect residue field, and let $T$ be an integral $\mathbb {Z}_p$-representation of $\mathrm {Gal}(\overline {K}/K)$. A theorem of T. Liu says that if $T/p^n T$ is torsion semistable (resp., crystalline) of uniformly bounded Hodge-Tate weights for all $n \geq 1$, then $T$ is also semistable (resp., crystalline). In this paper, we show that we can relax the condition of “uniformly bounded Hodge-Tate weights” to an unbounded (log-)growth condition.


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Additional Information

Hui Gao
Affiliation: Department of Mathematics and Statistics, University of Helsinki, FI-00014, Finland
MR Author ID: 1079735
Email: hui.gao@helsinki.fi

Keywords: Torsion Kisin modules, semi-stable representations
Received by editor(s): May 20, 2017
Received by editor(s) in revised form: November 1, 2017
Published electronically: March 30, 2018
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2018 American Mathematical Society