Spherical varieties and non-ordinary families of cohomology classes

We show that p-adic families of cohomology classes associated to symmetric spaces vary p-adically over small discs in weight space, without any ordinarity assumption. This generalises previous work of Loeffler, Zerbes and the author. Furthermore, we show that these families exhibit full variation in the cyclotomic direction, generalising previous constructions of Euler systems and p-adic L-functions. As an application we show that the Lemma–Flach Euler system of Loeffler–Skinner–Zerbes interpolates in Coleman families.