In this paper we study the non‐commutative scheme structure of the set of iso‐classes of simple modules on a finitely generated k‐algebra, k an algebraically closed field. We introduce the notion of geometric algebra and, referring to [12], we prove that these algebras are determined by the structure of this non‐commutative scheme. We consider natural completions of these schemes, adding indecomposable modules at infinity. This leads to a notion of correspondence on plane curves, which we explore to some degree. We end the paper with a sketch of how to relate global invariants of the algebra, like cyclic homology, to corresponding invariants of the scheme of simple finite‐dimensional modules.