---
_id: '53197'
abstract:
- lang: eng
text: This paper introduces the notion of locally algebraic representations and
corresponding sheaves in the context of the cohomology of arithmetic groups. These
representations are particularly relevant for studying integral structures and
special values of cohomological automorphic representations, as well as corresponding
period relations. We introduce and investigate related concepts such as locally
algebraic $(\lieg,K)$-modules and cohomological types of automorphic representations.
Applying the recently developed theory of tdos and twisted $\mathcal D$-modules,
we establish the existence of canonical global $1/N$-integral structures on spaces
of automorphic cusp forms. As an application, we define canonical periods attached
to regular algebraic automorphic representations, potentially related to the action
of Venkatesh's derived Hecke algebra on cuspidal cohomology.
author:
- first_name: Fabian
full_name: Januszewski, Fabian
id: '81636'
last_name: Januszewski
citation:
ama: Januszewski F. Locally algebraic representations and integral structures on
the cohomology of arithmetic groups. Published online 2024.
apa: Januszewski, F. (2024). *Locally algebraic representations and integral structures
on the cohomology of arithmetic groups*.
bibtex: '@article{Januszewski_2024, title={Locally algebraic representations and
integral structures on the cohomology of arithmetic groups}, author={Januszewski,
Fabian}, year={2024} }'
chicago: Januszewski, Fabian. “Locally Algebraic Representations and Integral Structures
on the Cohomology of Arithmetic Groups,” 2024.
ieee: F. Januszewski, “Locally algebraic representations and integral structures
on the cohomology of arithmetic groups.” 2024.
mla: Januszewski, Fabian. *Locally Algebraic Representations and Integral Structures
on the Cohomology of Arithmetic Groups*. 2024.
short: F. Januszewski, (2024).
date_created: 2024-04-03T17:16:53Z
date_updated: 2024-04-03T17:16:58Z
language:
- iso: eng
page: '69'
status: public
title: Locally algebraic representations and integral structures on the cohomology
of arithmetic groups
type: preprint
user_id: '81636'
year: '2024'
...