The Plectic Weight Filtration on Cohomology of Shimura Varieties and Partial Frobenius

TL;DR

This paper establishes a natural plectic weight filtration on the cohomology of Hilbert modular varieties, utilizing weight structures and partial Frobenius, and extends these concepts to compactifications.

Contribution

It introduces a plectic weight filtration on cohomology of Hilbert modular varieties and extends partial Frobenius to compactifications, advancing understanding of their structure.

Findings

Partial Frobenius extends to compactifications.

Construction of plectic weight filtration on cohomology.

Application of weight t-structures to Shimura varieties.

Abstract

We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekovar and Scholl. This is achieved with the help of Morel's work on weight t-structures and a detailed study of partial Frobenius. We prove in particular that the partial Frobenius extends to toroidal and minimal compactifications.