Hecke Eigensystems for (mod p) Modular Forms of PEL-type and Algebraic Modular Forms

Details Hecke Eigensystems for (mod p) Modular Forms of PEL-type and Algebraic Modular Forms Hecke Eigensystems for (mod p) Modular Forms of PEL-type and Algebraic Modular Forms

2011-01-17

arxiv.org/abs/1101.3143v2

Mathematics

Number Theory

46 pages. Comments are welcome

Scientific paper

10.1093/imrn/rns114

We show that, under suitable assumptions, the systems of Hecke eigenvalues arising from (mod p) modular forms of PEL-type associated to an algebraic group G of type A or C coincide with the Hecke eigensystems arising from (mod p) algebraic modular forms for an inner form of G. We treat explicitly the case of unitary groups, and we give in this case an asymptotic formula for the number of eigensystems. The paper generalizes results of J-P. Serre for GL(2) and A. Ghitza for GSp(2g).

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