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Limit of torsion semistable Galois representations with unbounded weights

Author: Hui Gao
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 11F80, 11F33
Published electronically: March 30, 2018
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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 $ \textup {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

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

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