Relations between Dieudonné displays and crystalline Dieudonné theory

Lau, Eike

doi:10.2140/ant.2014.8.2201

Cited by 52 publications

(91 citation statements)

References 20 publications

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“…Later Lau [19] and Liu [20] independently proved that the statement also holds for p 2, which in fact was the original motivation of the note of Breuil [3]. For the convenience of the reader, here is a very rough sketch of how the equivalence of the theorem works.…”

Section: Annales De L'institut Fouriermentioning

confidence: 93%

Models of group schemes of roots of unity

Mézard¹,

Romagny²,

Tossici³

2013

Ann. inst. Fourier

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Let O K be a discrete valuation ring of mixed characteristics p0, pq, with residue field k. Using work of Sekiguchi and Suwa, we construct some finite flat O K -models of the group scheme µ p n ,K of p n -th roots of unity, which we call Kummer group schemes. We carefully set out the general framework and algebraic properties of this construction. When k is perfect and O K is a complete totally ramified extension of the ring of Witt vectors W pkq, we provide a parallel study of the Breuil-Kisin modules of finite flat models of µ p n ,K , in such a way that the construction of Kummer groups and Breuil-Kisin modules can be compared. We compute these objects for n ď 3. This leads us to conjecture that all finite flat models of µ p n ,K are Kummer group schemes.

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Section: Annales De L'institut Fouriermentioning

confidence: 93%

Models of group schemes of roots of unity

Mézard¹,

Romagny²,

Tossici³

2013

Ann. inst. Fourier

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“…It should be mentioned that a classification of finite flat group schemes via Kisin modules is also proved for p = 2 by Kisin [22] for the case of unipotent finite flat group schemes and independently by Kim [19], Lau [23] and Liu [26] for the general case. However, the author does not know whether a similar correspondence of ramification between characteristic zero and two holds for finite flat group schemes with non-trivial multiplicative parts.…”

Section: Then the Natural Isomorphism Of G K ∞ -Modules G(m)(ok )| mentioning

confidence: 99%

Ramification correspondence of finite flat group schemes over equal and mixed characteristic local fields

Hattori¹

2012

Journal of Number Theory

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Let p > 2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fraction field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O K and k [[u]], respectively. In this paper, we show the ramification subgroups of G and H in the sense of Abbes-Saito are naturally isomorphic to each other when they are associated to the same Kisin module.

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“…When p = 2, again, most of this follows [11]. However, the results of Lau from [16] lead to a uniform proof in all cases, and, more importantly, also at the same time give us the functors P a classifying p-divisible groups over the artinian rings To begin, the existence of the functors M and P a , as well as the compatibility between them asserted in (2.12.1) follows from [16 4.2)], but the assertion there is off by a Tate twist.) An independent proof of this assertion, which also works when p = 2, has been given by Lau in [15].…”

Section: 11mentioning

confidence: 93%

“…The nontrivial input is Lau's classification of p-divisible groups over a very large class of 2-adic rings in terms of Dieudonné displays [16], and its compatibility with a p-adic Hodge theoretic construction of Kisin [15].…”

Section: Introductionmentioning

confidence: 99%