Towards an explicit eigencurve for GL(3)
نویسندگان
چکیده
Starting with a numerically non-critical (at p) Hecke eigenclass f in the homology of a congruence subgroup Γ of SL3(Z) (where p divides the level of Γ) with classical coefficients, we first show how to compute to any desired degree of accuracy a lift of f to a Hecke eigenclass F with coefficients in a module of p-adic distributions. Then we show how to find to any desired degree of accuracy the germ of the projection to weight space of the eigencurve Z around the point z corresponding to the system of Hecke eigenvalues of F . We do this under the conjecturally mild hypothesis that Z is smooth at z.
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