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Eisenstein congruences for split reductive groups

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Abstract

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.

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Bergström, J., Dummigan, N. Eisenstein congruences for split reductive groups. Sel. Math. New Ser. 22, 1073–1115 (2016). https://doi.org/10.1007/s00029-015-0211-0

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