Eisenstein congruences for split reductive groups

Research paper by Jonas Bergström, Neil Dummigan

Indexed on: 02 Jul '16Published on: 26 Nov '15Published in: Selecta Mathematica


We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values of certain L-functions. We examine the consequences in several special cases and use the Bloch–Kato conjecture to further motivate a belief in the congruences.