P-torsion étale sheaves on the Jacobian of a curve

Abstract

Suppose X is a smooth, proper, geometrically connected curve over Fq with an Fq-rational point x0. For any Fq×-character σ of π1(X) trivial on x0, we construct a functor Lnσ from the derived category of coherent sheaves on the moduli space of deformations of σ over the Witt ring Wn(Fq) to the derived category of constructible Wn(Fq)-sheaves on the Jacobian of X. The functors Lnσ categorify the Artin reciprocity map for geometric class field theory with p-torsion coefficients. We then give a criterion for the fully faithfulness of (an enhanced version of) Lnσ in terms of the Hasse–Witt matrix of X.