Spherical varieties and p-adic families of cohomology classes

2021/06/30 by Loeffler, David, Rockwood, Rob, Zerbes, Sarah Livia · 1 citation
#11F67 #11R23 #14M17 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.16082

Abstract

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 Grössencharacters 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 GSp(4), GSp(4) x GL(2), and GSp(4) x GL(2) x GL(2).

Cited by

• On quaternionic ordinary families of modular forms and p-adic L-functions

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• Spherical varieties and non-ordinary families of cohomology classes
• Norm-compatible systems of Galois cohomology classes for GSp₆
• Some norm relations of the Eisenstein classes of GSp(4)
• Rankin-Selberg Euler systems and p-adic interpolation
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