  We give a generic spectral decomposition of the derived category of twisted
D-modules on a moduli stack of mirabolic vector bundles on a curve X in
characteristic p: that is, we construct an equivalence with the derived
category of quasi-coherent sheaves on a moduli stack of mirabolic local systems
on X. This equivalence may be understood as a tamely ramified form of the
geometric Langlands equivalence. When X has genus 1, this equivalence
generically solves (in the sense of noncommutative geometry) the quantum
Calogero-Moser system.
