Hecke eigensystems of automorphic forms (mod p) of Hodge type and algebraic modular forms
نویسندگان
چکیده
We show that the systems of prime-to-p Hecke eigenvalues arising from automorphic forms $$\pmod p$$ for a good prime p associated to an algebraic group $$G/{\mathbb {Q}}$$ Hodge type are same as those modular inner form G.
منابع مشابه
Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...
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In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
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. The constants are effectively computable. Proof. Part (a) follows from the fact that the algebraic group GSp2g has dimension 2g +g+1. Part (b) is obvious. Combined with Theorem 1.1 of [Ghi04], Theorem 1 gives Corollary 3 (Algebraic modular forms). Let B/Q be the quaternion algebra ramified at p and ∞. The number of systems of Hecke eigenvalues coming from algebraic modular forms (mod p) of le...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2021
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-021-02200-y