Limit of torsion semistable Galois representations with unbounded weights

Gao, Hui

doi:10.1090/proc/14044

Limit of torsion semistable Galois representations with unbounded weights
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Proc. Amer. Math. Soc. 146 (2018), 3275-3283 Request permission

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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