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

Abstract

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).

46 pages. Comments are welcome

References in corpus (2)

• Siegel modular forms (mod p) and algebraic modular forms
• On the Tate and Langlands--Rapoport conjectures for special fibres of integral canonical models of Shimura varieties of abelian type

Cited by in corpus (3)

• Arithmetic Satake compactifications and algebraic Drinfeld modular forms
• Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms
• On arithmetic of the superspecial locus