Equivariant line bundles with connection on the Drinfeld upper half-space Ω⁽²⁾

Ardakov and Wadsley developed a theory of $\mathscr{D}$-modules on rigid analytic spaces and established a Beilinson-Bernstein style localisation theorem for coadmissible modules over the locally analytic distribution algebra. Using this theory, they obtained admissible locally analytic representations of GL₂ by studying equivariant line bundles with connection on the Drinfeld half-plane Ω⁽¹⁾. In this thesis, we will follow the idea of Ardakov-Wadsley and extend their techniques to GL₃ by studying the Drinfeld upper half-space Ω⁽²⁾ of dimension 2.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Zhu, Yiyue

Advisor dc:contributor.advisor

• Wadsley, Simon

• Drinfeld half-space
• locally analytic representation
• p-adic

Licence

• https://www.repository.cam.ac.uk/bitstreams/1a098187-5c5e-451a-b215-5cd2c3fa5fa5/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.106950

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/365880