D-modules on 1|1 supercurves

Abstract

a b s t r a c tIt is known that to every (1|1)-dimensional supercurve X there is associated a dual supercurveX , and a superdiagonal ∆ ⊂ X ×X. We establish that the categories of D-modules on X ,X and ∆ are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a super elliptic curve.