We consider a Hida family of nearly ordinary cusp forms on a quaternion algebra defined over a totally real number field. The aim of this work is to construct a cohomology class with coefficients in a -adic sheaf over an Iwasawa algebra that can be specialized to cohomology classes attached to classical cusp forms in the given Hida family. Our result extends the work of Greenberg and Stevens on modular symbols attached to ordinary Hida families when the ground field is the field of rational numbers.
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Baskar Balasubramanyam, Matteo Longo, Λ-adic modular symbols over totally real fields. Comment. Math. Helv. 86 (2011), no. 4, pp. 841–865