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

We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekov\'a\v r 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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2020

Author dc:creator

• Wu, Zhiyou

Advisor dc:contributor.advisor

• Scholl, Anthony

• Shimura varieties
• Hodge theory
• number theory

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/5535acc8-0ad2-46cc-8cd1-c892429e0be2/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.48566

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/301493