The geometric correspondence for singular curves

The aim of this article is to give a translation of the geometric Langlands correspondence for singular curves. We will first be interested in finding a good notion of connection on singular curves. This will lead us to the notion of ‘mild singularities’. We will then restrict ourselves to curves with only mild singularities and we will find a consistent translation of the Hecke correspondence. The proof will need generalised jacobians and the introduction of ‘level structures’ (Section 3).