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Arithmetic Breuil-Kisin-Fargues modules and several topics in p-adic Hodge theoryHeng Du (10717026) 06 May 2021 (has links)
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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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