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Singular support for categories over a scheme

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 26, 2019 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Dmytro Arinkin (University of Wisconsin-Madison)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • microlocal categories

  • geometric Langlands conjecture

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Abstract

Some geometric objects can be studied `microlocally': instead of just looking at their support (the set of points where an object is non-trivial), one can consider their `singular support', which remembers the `direction' of non-trivial behavior. Examples include the wave front of a distribution, the singular support of a constructible sheaf, and the characteristic variety of a D-module. Another important example of such `microlocal' theory is singular support of (ind-)coherent sheaves, which plays an important role in the global geometric Langlands program. In my talk, I will present a higher categorical analogue of this: the theory of singular support for categories over a scheme, which is important for the local Langlands program.

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