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

We prove that any Hecke eigenclass in the mod p cohomology of a congru ence 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.