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arXiv · 1302.1888

Compatibility of Kisin modules for different uniformizers

Tong Liu
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Abstract

Let p be a prime and T a lattice inside a semi-stable representation V. We prove that Kisin modules associated to T by selecting different uniformizers are isomorphic after tensoring a subring in W(R). As consequences, we show that several lattices inside the filtered (phi, N)-module of V constructed from Kisin modules are independent on the choice of uniformizers. Finally we use a similar strategy to show that the Wach module can be recovered from the (φ, \hat G)-module associated to T when V is crystalline and the base field is unramified.

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Tong Liu. 2013-02-07. Compatibility of Kisin modules for different uniformizers. https://arxiv.org/abs/1302.1888

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