Représentations cristallines dans le cas d’un corps résiduel imparfait

Brinon, Olivier

doi:10.5802/aif.2205

Cited by 27 publications

(67 citation statements)

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“…We will recall the construction of rings of p-adic periods Fontaine [Fon94a], which is functorial with respect to C p and K. We also recall abstract algebraic properties of these rings as in [Bri06]. Although we do not assume K = K, standard techniques of proofs in the case K = K, which are developed in [Fon94a,Bri06], can be applied to our situation.…”

Section: Basic Construction Of Rings Of P-adic Periodsmentioning

confidence: 99%

“…For the reader interested in these structures, see [Bri06,3.5] for example. We need only the connection on D dR for the proof of Main Theorem: The finite K-vector…”

Section: Calculations Of H 0 and Verification Of G K -Regularitiesmentioning

confidence: 99%

“…The notions of the above categories of representations are defined by Olivier Brinon when k K admits a finite p-basis ( [Bri06]). In this case, the p-adic monodromy theorem is proved by Kazuma Morita ([Mor, Corollary 1.2]).…”

Section: Introductionmentioning

confidence: 99%

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The p-adic monodromy theorem in the imperfect residue field case

Ohkubo

2013

Algebra Number Theory

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Let K be a complete discrete valuation field of mixed characteristic (0, p) and GK the absolute Galois group of K. In this paper, we will prove the p-adic monodromy theorem for p-adic representations of GK without any assumption on the residue field of K, for example the finiteness of a p-basis of the residue field of K. The main point of the proof is a construction of (ϕ, GK )-module N ∇+ rig (V ) for a de Rham representation V , which is a generalization of Pierre Colmez' N

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Section: Basic Construction Of Rings Of P-adic Periodsmentioning

confidence: 99%

“…For the reader interested in these structures, see [Bri06,3.5] for example. We need only the connection on D dR for the proof of Main Theorem: The finite K-vector…”

Section: Calculations Of H 0 and Verification Of G K -Regularitiesmentioning

confidence: 99%

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The p-adic monodromy theorem in the imperfect residue field case

Ohkubo

2013

Algebra Number Theory

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“…See also [5,7,10,12,13] and [25]. Throughout this section, fiber products of fine log schemes are always considered in the category of fine log schemes (cf.…”

Section: Hodge-tate Representationsmentioning

confidence: 99%

Purity for Hodge-Tate representations

Tsuji

2010

Math. Ann.

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We prove that a kind of purity holds for Hodge-Tate representations of the fundamental group of the generic fiber of a semi-stable scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field. As an application, we see that the relative p-adic étale cohomology with proper support of a scheme separated of finite type over the generic fiber is Hodge-Tate if it is locally constant.

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“…La the Âorie des repre Âsentations cristallines a e Âte Â de Âcrite dans [7], et fait l'objet de rappels dans la section 3. On construit des anneaux et des foncteurs analogues a Á ceux de Kisin.…”

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