GALOIS REPRESENTATIONS AND HECKE OPERATORS ASSOCIATED WITH THE MOD p COHOMOLOGY OF GL(1,Z) AND GL(2,Z)

Abstract

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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