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 , 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.
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