The <i>p</i>-adic monodromy theorem in the imperfect residue field case

Ohkubo, Shun

doi:10.2140/ant.2013.7.1977

Cited by 10 publications

(23 citation statements)

References 17 publications

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“…3.3.1, allows him to obtain the first proof of p-adic local monodromy theorem in the imperfect residue field case: namely, V is de Rham if and only it is potentially semi-stable. Alternatively, another proof which works even when [k : k p ] = +∞ is supplied by [Ohk13].…”

Section: Morita's Resultsmentioning

confidence: 99%

“…For example, Brinon studies the Hodge-Tate, de Rham, and crystalline representations in the imperfect residue field case in [Bri06], which then pave the way for the studies in the relative case in [Bri08]. For another example, very recently, Shimizu proves a variant of p-adic local monodromy theorem in the relative case in [Shi]; the proof makes crucial use of p-adic local monodromy theorem in the imperfect residue field case established in [Mor14,Ohk13].…”

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confidence: 99%

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On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case

Gao

2021

Preprint

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Let K be a mixed characteristic complete discrete valuation field with residue field admitting a finite p-basis, and let G K be the Galois group. Inspired by Liu and Zhu's construction of p-adic Simpson and Riemann-Hilbert correspondences over rigid analytic varieties, we construct such correspondences for representations of G K . As an application, we prove a Hodge-Tate (resp. de Rham) "rigidity" theorem for p-adic representations of G K , generalizing a result of Morita. Contents 1. Introduction 1 2. Fontaine rings and Fontaine modules 6 3. Change of base fields 11 4. Sen theory and Tate-Sen decompletion 13 5. p-adic Simpson correspondence and Hodge-Tate rigidity 18 6. Sen-Fontaine theory 22 7. p-adic Riemann-Hilbert correspondence and de Rham rigidity 25 References 27

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Section: Morita's Resultsmentioning

confidence: 99%

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confidence: 99%

On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case

Gao

2021

Preprint

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“…The notations below depend on various choices, particularly that of K 0 and ϕ. The way these choices are made are slightly different in the references [Bri06], [BT08], [Mor10,Mor14] and [Ohk13]. But they are all "equivalent" definitions, cf.…”

Section: Fontaine Modules and Semi-stable Representationsmentioning

confidence: 99%

Integral $p$-adic Hodge theory in the imperfect residue field case

Gao¹

2020

Preprint

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Let K be a mixed characteristic complete discrete valuation field with residue field admitting a finite p-basis, and let G K be the Galois group. We first classify semi-stable representations of G K by weakly admissible filtered (ϕ, N )-modules with connections. We then construct a fully faithful functor from the category of integral semi-stable representations of G K to the category of Breuil-Kisin G K -modules. Using the integral theory, we classify p-divisible groups over the ring of integers of K by minuscule Breuil-Kisin modules with connections. Contents1. Introduction 1 2. Fontaine modules and semi-stable representations 4 3. Modification of Fontaine modules 10 4. Integral p-adic Hodge theory 13 5. Modules over S and S 19 6. Breuil-Kisin modules and p-divisible groups 22 References 28

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“…Step 1 of the proof of the main theorem of [Ohkubo 2013] that the inertia I K acts on V i via a finite quotient, i.e., V i ∈ Rep f.g.…”

Section: Mspmentioning

confidence: 99%