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D-modules on singular varieties

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  • UserHaiping Yang, Imperial College London
  • ClockFriday 21 February 2020, 15:00-16:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Matthew Conder.

The category of D-modules on smooth varieties are well understood. In this talk, we work with a particular compact generator of the (derived) category of D-modules on a singular variety X. Hence we get a derived equivalence and we can view D-modules as DG-modules over a particular DG-algebra. In the case that the variety only consists of cuspidal singularities, we get an abelian Morita equivalence between D-modules on X and modules over the sheaf of differential operators Diff(X). From this, there is a certain cohomology sheaf on X which is non-vanishing if and only if X is smooth or cuspidal. Hence, to a certain extent, we can ‘detect’ the singularity of X by looking at this

This talk is part of the Junior Algebra and Number Theory seminar series.

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