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<p>Let K be a discrete valuation field with perfect residue field, we study the functor from
weakly admissible filtered (φ,N,G<sub>K</sub>)-modules over K to the isogeny category of Breuil-
Kisin-Fargues G<sub>K</sub>-modules. This functor is the composition of a functor defined by Fargues-Fontaine from weakly admissible filtered (φ,N,G<sub>K</sub>)-modules to G<sub>K</sub>-equivariant modifications of vector bundles over the Fargues-Fontaine curve X<sub>FF</sub> , with the functor of Fargues-Scholze that between the category of admissible modifications of vector bundles over X<sub>FF</sub>
and the isogeny category of Breuil-Kisin-Fargues modules. We characterize the essential
image of this functor and give two applications of our result. First, we give a new way of
viewing the p-adic monodromy theorem of p-adic Galois representations. Also we show our
theory provides a universal theory that enable us to compare many integral p-adic Hodge theories at
the A<sub>inf</sub> level.
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| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/14502945 |
| Date | 06 May 2021 |
| Creators | Heng Du (10717026) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Arithmetic_Breuil-Kisin-Fargues_modules_and_several_topics_in_p-adic_Hodge_theory/14502945 |
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