A canonical generator for congruence ideals of Hida families

2023/12/27 by Maksoud, Alexandre
#11R27 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.16706

Abstract

We construct canonical adjoint p-adic L-functions generating the congruence ideal attached to Hida families using Ohta's pairing. We show that these p-adic L-functions, suitably modified by certain Euler factors, are interpolated by a regular element of Hida's universal ordinary Hecke algebra. We also relate them to characteristic series of primitive adjoint Selmer groups.

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