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Spherical varieties and p-adic families of cohomology classes
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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 Gr\"ossencharacters 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).
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The Asai--Flach Euler system in $p$-adic families
The Asai-Flach Euler system of Lei-Loeffler-Zerbes is interpolated p-adically over Hida families of Hilbert modular forms over real quadratic fields.
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