Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, ZZ) with Twisted Coefficients
نویسندگان
چکیده
1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.
منابع مشابه
Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients
1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.
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We prove that any Hecke eigenclass in the mod p cohomology of a congruence subgroup of GL(1,Z) or GL(2,Z) has attached to it a mod p Galois representation such that the characteristic polynomial of a Frobenius element at a prime l equals the Hecke polynomial at l.
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Ash's research was partially supported by NSF Grant DMS-8919696. Conjecturally, any “algebraic” automorphic representation on GL(n) should have an n-dimensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology overC of congruence subgroups of GL(n;Z). On the other hand, the first author has conjectured that for any Hecke eigenclass ...
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In this paper we give additional computational evidence for the generalization of Serre’s Conjecture [Serre 87] proposed in [Ash-Sinnott 00] and extended in [Ash-Doud-Pollack 02]. We also propose a further refinement — corresponding precisely to the “peu ramifiée – très ramifiée” distinction in Serre — which removes an ambiguity in the prediction of the earlier conjecture. The conjecture sets o...
متن کامل- EXTENSIONS OF Q AND THE MOD p COHOMOLOGY OF GL 3 ( Z )
In this paper we give additional computational evidence for the generalization of Serre’s Conjecture [Serre 87] proposed in [Ash-Sinnott 00] and extended in [Ash-Doud-Pollack 02]. We also propose a further refinement — corresponding precisely to the “peu ramifiée – très ramifiée” distinction in Serre — which removes an ambiguity in the prediction of the earlier conjecture. The conjecture sets o...
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تاریخ انتشار 1998