Proof of the geometric Langlands conjecture V: the multiplicity one theorem

Abstract: This is the final paper in the series of five, in which we prove the geometric Langlands conjecture (GLC). We conclude the proof of GLC by showing that there exists a unique (up to tensoring up by a vector space) Hecke eigensheaf corresponding to an irreducible local system (hence, the title of the paper). We achieve this by analyzing the geometry of the stack of local systems.