A finiteness result for the compactly supported cohomology of rigid analytic varieties, II

Huber, Roland

doi:10.5802/aif.2283

Cited by 19 publications

(53 citation statements)

References 16 publications

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“…By Lemma 4.28 (iv), we may assume that X is affine. Then the isomorphy of ξ X follows from [19,Lemma 2.13].…”

Section: Compactly Supported Cohomology and Rψ X C λmentioning

confidence: 99%

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Variants of formal nearby cycles

Mieda¹

2013

J. Inst. Math. Jussieu

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Abstract. In this paper, we introduce variants of formal nearby cycles for a locally noetherian formal scheme over a complete discrete valuation ring. If the formal scheme is locally algebraizable, then our nearby cycle gives a generalization of Berkovich's formal nearby cycle. Our construction is entirely scheme-theoretic and does not require rigid geometry. Our theory is intended for applications to the local study of the cohomology of Rapoport-Zink spaces.

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“…By Lemma 4.28 (iv), we may assume that X is affine. Then the isomorphy of ξ X follows from [19,Lemma 2.13].…”

Section: Compactly Supported Cohomology and Rψ X C λmentioning

confidence: 99%

“…(iii) If X is locally algebraizable (Definition 3. 19) or adic over Spf R, then RΨ X Λ := RΨ X ,(∅,X s ) Λ is canonically isomorphic to Berkovich's formal nearby cycle for X .…”

Section: Introductionmentioning

confidence: 99%

Variants of formal nearby cycles

Mieda¹

2013

J. Inst. Math. Jussieu

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“…We notice that, if the characteristic of k is zero, finiteness of the cohomology groups and constructibility of the vanishing cycles sheaves for locally finitely presented formal schemes and for formal completion of them along a subscheme of the closed fiber were proved by Roland Huber in [Hub1] and [Hub2].…”

Section: Introductionmentioning

confidence: 97%

Finiteness theorems for vanishing cycles of formal schemes

Berkovich

2015

Isr. J. Math.

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Let k be a non-Archimedean field with nontrivial valuation, and k • its ring of integers. In this paper we prove constructibility of vanishing cycles sheaves for arbitrary formal schemes locally finitely presented over k • as well as special formal schemes over k • (for discretely valued k). This allows us to extend continuity results, established earlier for locally algebraic formal schemes, to the whole classes of formal schemes.

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“…[7] 10.1/3 and [45] Theorem 4). Let us note that R-envelopes already appeared in [38] and in [27] under the name of quasi-compactifications. In order to rigorously implement the strategy of proof outlined above, we first have to establish a number of preliminary results in analytic arithmetic geometry which may be of independent interest.…”

Section: Introductionmentioning

confidence: 99%