GALOIS REPRESENTATIONS AND HECKE OPERATORS ASSOCIATED WITH THE MOD p COHOMOLOGY OF GL(1,Z) AND GL(2,Z)
نویسندگان
چکیده
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.
منابع مشابه
Galois representations from the cohomology of SL(3, Z)
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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1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.
متن کاملGalois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, ZZ) with Twisted Coefficients
1991 Mathematics Subject Classi cation. Primary: 11F75. Secondary: 11F67, 12F12.
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Let p be a prime number and F an algebraic closure of the finite field Fp with p elements. Let n and N denote positive integers, N prime to p. We are interested in representations of the Galois group GQ = Gal(Q̄/Q) into GL(n,F), unramified at all finite primes not dividing pN . (We shall say “ρ is unramified outside pN .”) In this paper, “representation” will always mean “continuous, semisimple ...
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