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# Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

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Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2018, Issue 740

# Compatibility of Kisin modules for different uniformizers

Tong Liu
• Department of Mathematics, Purdue University, 150 North University Street, West Lafayete, Indiana 47907-2067, USA
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Published Online: 2015-12-18 | DOI: https://doi.org/10.1515/crelle-2015-0074

## 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 $W\left(R\right)$. As consequences, we show that several lattices inside the filtered $\left(\phi ,N\right)$-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 $\left(\phi ,\stackrel{^}{G}\right)$-module associated to T when V is crystalline and the base field is unramified.

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## About the article

Published Online: 2015-12-18

Published in Print: 2018-07-01

Funding Source: National Science Foundation

Award identifier / Grant number: DMS-0901360

Award identifier / Grant number: DMS-1406926

The author is partially supported by NSF grants DMS-0901360 and DMS-1406926.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 740, Pages 1–24, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102,

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