This tag is for questions relating to -Modules.
The origin of -modules is in the work of the Japanese school of Mikio Sato in the mid-twentieth century on algebraic analysis. The aim of this program was to understand systems of linear partial differential equations on manifolds, and their generalizations, using the techniques of algebraic geometry and sheaf theory.
A -module on an (algebraic or complex analytic) variety X is the notion generalising the one of finite rank vector bundles with flat connection.
The theory of algebraic -modules provides a bridge from algebra to analysis and topology. It can be regarded as "mildly non-commutative algebra" in the sense that it is obtained by extending the methods of commutative algebra to non-commutative rings (or rather sheaves of rings) of algebraic differential operators on complex varieties. As such it gives a substitute in algebraic geometry for the theory of linear partial differential equations.
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