Spherical varieties and non-ordinary families of cohomology classes
Year: 2025
Type: article
Abstract: We give a construction of non-ordinary $p$-adic families of classes in the cohomology of locally symmetric spaces associated to spherical pairs of reductive groups. In the étale case, we show how to map these classes into Galois cohomology. The methods developed in this paper can be used to give new constructions of $p$-adic families of Euler systems and $p$-adic $L$-functions. As an example, we show how the constructions of this paper can be used to construct norm-compatible classes associated to non-ordinary Siegel modular forms, generalising $p$-part of the Lemma--Flach Euler system constructed by Loeffler--Skinner--Zerbes.
Source: Journal of Number Theory
Author: Rob Rockwood
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7083174896