Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families

Let f and g be two cuspidal modular forms and let F be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space W . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over V×W that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms in the critical range (i.e, the range where the p-adic L-function 𝐿𝑝 interpolates critical values of the global L-function). We show that the support of this sheaf is contained in the vanishing locus of 𝐿𝑝 .