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

Graham, A
Gulotta, D
Xu, Y

17 July 2020

## Last Updated:

2021-07-26T11:07:43.807+01:00

## DOI:

10.4153/S0008414X2000019X

## abstract:

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 .

1094857

Submitted

Journal Article