Poincaré duality for rigid analytic Hyodo--Kato theory

Ertl, Veronika; Yamada, Kazuki

doi:10.48550/arxiv.2009.09160

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2022

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“…In this section, we recall from [CD12, DM15] that any monoidal algebraic realization is automatically equipped with some formal structures of a Weil cohomology, such as Poincaré duality and a formalism of Chern classes. For such structures on Hyodo-Kato cohomology, see also [NN16, Section 5], [EY20], [LP16]. Definition 3.15.…”

Section: 1mentioning

confidence: 99%

On the p-adic weight-monodromy conjecture for complete intersetions in toric varieties

Binda¹,

Kato²,

Vezzani³

2022

Preprint

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We give a proof of the p-adic weight monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze's proof in the ℓ-adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives CONTENTS 1. Introduction 1 Acknowledgments 5 2. Log motives and rigid motives 5 3. The motivic Hyodo-Kato realization 15 4. Motivic existence of tubular neighborhoods 24 5. The p-adic weight-monodromy for complete intersections 25 Appendix A. A log-free Hyodo-Kato cohomology 28 References 32

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confidence: 99%