Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families

2019/05/31 by Andrew Graham, Daniel R. Gulotta, Yujie Xu
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.4153/s0008414x2000019x

Abstract

Abstract Let f and g be two cuspidal modular forms and let \mathcal F be a Coleman family passing through f , defined over an open affinoid subdomain V of weight space \mathcal W . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over V × \mathcal 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 L_p interpolates critical values of the global L -function). We show that the support of this sheaf is contained in the vanishing locus of L_p .

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