Spherical varieties and p-adic families of cohomology classes

TY - JOUR

T1 - Spherical varieties and p-adic families of cohomology classes

AU - Rockwood, Robert

AU - Loeffler, David

AU - Zerbes, Sarah

PY - 2024

Y1 - 2024

N2 - We prove a “twist-compatibility” result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology classes of many different weights, including twists by Grossencharacters of possibly non-trivial infinity-type. This subsumes and generalises a number of prior results relating to Euler systems and p-adic L-functions, and we conclude with some novel applications to Euler systems for GSp4, GSp4 × GL2, and GSp4 × GL2 × GL2.

AB - We prove a “twist-compatibility” result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology classes of many different weights, including twists by Grossencharacters of possibly non-trivial infinity-type. This subsumes and generalises a number of prior results relating to Euler systems and p-adic L-functions, and we conclude with some novel applications to Euler systems for GSp4, GSp4 × GL2, and GSp4 × GL2 × GL2.

KW - Euler systems

KW - p-adic L-functions

KW - Shimura varieties

M3 - Article

JO - Elliptic curves and modular forms in arithmetic geometry – celebrating Massimo Bertolini's 60th birthday

JF - Elliptic curves and modular forms in arithmetic geometry – celebrating Massimo Bertolini's 60th birthday

ER -