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

Abstract

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