# Can one calculate Ext's between microlocalized perverse sheaves/D-modules using topology?

So, I know one really good technique for calculating Ext's between perverse sheaves/D-modules using topology: the convolution algebra formalism, worked out in great detail in the book of Chriss and Ginzburg. This method has some great successes in geometric representation theory: the most popular is probably Springer theory and character sheaves.

The rough idea of this technique is that just as the Ext algebra of the constant sheaf on a topological space with itself is the cohomology of the space (and the Yoneda product is cup product), Ext's between pushforwards of constant sheaves can be calculated using the Borel-Moore homology of fiber products, and Yoneda product will again have a realization as convolution product.

Now, I'm interested in pushing this method a bit further to work in the microlocal world. Microlocal perverse sheaves/D-modules are a new geometric category, where one forgets about some closed subset of the cotangent bundle, and declares any map which is an isomorphism on vanishing cycles (which are microlocal stalks) away from this locus to be an isomorphism.

My question: If I have a constant sheaf (in D-module language, the D-module of functions) on a smooth variety, or maybe a pushforward of one, is there some way of calculating the Ext's in the microlocal category topologically as well, hopefully using the topology of the characteristic variety?

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