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We find the model completion of the theory modules over $A$, where $A$ is afinitely generated commutative algebra over a field $K$. This is done in acontext where the field $K$ and the module are represented by sorts in thetheory, so that constructible sets associated with a module can be interpretedin this language. The language is expanded by additional sorts for theGrassmanians of all powers of $K^n$, which are necessary to achieve quantifierelimination.  The result turns out to be that the model completion is the theory of acertain class of ``big'' injective modules. In particular, it is shown that theclass of injective modules is itself elementary. We also obtain an explicitdescription of the types in this theory.Comment: AMSLaTeX, 13 pages, no figures. Part of author's phd thesi

The model completion of the theory of modules over finitely generated commutative algebras