Une g�n�ralisation de la th�orie de Sen

Brinon, Olivier

doi:10.1007/s00208-003-0472-3

Cited by 17 publications

(32 citation statements)

References 3 publications

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“…Then, the assertion follows from the following relations which are easy to compute (cf. [1,Proposition 7]…”

Section: Hyodo's Calculation and Sen's Theorymentioning

confidence: 99%

“…Let the notation be as in [1]. In this appendix, we point out the following errors in the paper [1] and give the argument to fix them.…”

Section: Proof Of Proposition 72 Recall Construction 52 Applying Tmentioning

confidence: 99%

“…) is an isomorphism [1,Théorème 5(i)]. Here, the LHS is the continuous Galois cohomology and the RHS is the Lie algebra cohomology.…”

mentioning

confidence: 99%

“…8, we prove Main Theorem: We construct a morphism of δ-functors ι : H • (g K ∞ , D Sen (−)) → K ∞ ⊗ K H • cont (G K , −) and prove this is an isomophism by a dévissage argument. Section 9 is an erratum for Brinon's paper [1].…”

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confidence: 99%

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A note on Sen’s theory in the imperfect residue field case

Ohkubo

2010

Math. Z.

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In Sen's theory in the imperfect residue field case, Brinon defined a functor from the category of C p -representations to the category of linear representations of a certain Lie algebra. We give a comparison theorem between the continuous Galois cohomology of C p -representations and the Lie algebra cohomology of the associated representations. The key ingredients of the proof are Hyodo's calculation of Galois cohomology and the effaceability of Lie algebra cohomology for solvable Lie algebras.

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“…Then, the assertion follows from the following relations which are easy to compute (cf. [1,Proposition 7]…”

Section: Hyodo's Calculation and Sen's Theorymentioning

confidence: 99%

“…Let the notation be as in [1]. In this appendix, we point out the following errors in the paper [1] and give the argument to fix them.…”

Section: Proof Of Proposition 72 Recall Construction 52 Applying Tmentioning

confidence: 99%

“…) is an isomorphism [1,Théorème 5(i)]. Here, the LHS is the continuous Galois cohomology and the RHS is the Lie algebra cohomology.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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A note on Sen’s theory in the imperfect residue field case

Ohkubo

2010

Math. Z.

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“…la C-représentation (cf. [4]) associée est triviale. Ses endomorphismes de Sen sont donc triviaux : l'action de l'inertie I K est donc finie (cf.…”

Section: Représentations De Dimensionunclassified

Représentations cristallines dans le cas d’un corps résiduel imparfait

Brinon¹

2006

Ann. inst. Fourier

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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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Une g�n�ralisation de la th�orie de Sen

Cited by 17 publications

References 3 publications

A note on Sen’s theory in the imperfect residue field case

A note on Sen’s theory in the imperfect residue field case

Représentations cristallines dans le cas d’un corps résiduel imparfait

Purity for Hodge-Tate representations

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