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

TL;DR

This paper proves the p-adic weight-monodromy conjecture for complete intersections in toric varieties by adapting Scholze's proof from the $-adic setting using homotopical methods in rigid analytic motives.

Contribution

It introduces a novel adaptation of Scholze's proof to the p-adic context employing homotopical techniques within rigid analytic motives.

Findings

Proof of the p-adic weight-monodromy conjecture for complete intersections in toric varieties

Development of homotopical methods in rigid analytic motives

Extension of Scholze's $-adic proof to the p-adic setting

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 $\ell$-adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives.