Singular support for categories over a scheme
Location: MSRI: Simons Auditorium
geometric Langlands conjecture
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.