Locally algebraic representations and integral structures on the cohomology of arithmetic groups
Januszewski, Fabian
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.
2024
info:eu-repo/semantics/preprint
doc-type:preprint
text
http://purl.org/coar/resource_type/c_816b
https://ris.uni-paderborn.de/record/53197
Januszewski F. Locally algebraic representations and integral structures on the cohomology of arithmetic groups. Published online 2024.
eng
info:eu-repo/semantics/closedAccess