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David Ben-Zvi, RLM 9.166: The Local Langlands Correspondence and Coherent Springer Theory
Thursday, September 12, 2019, 03:30pm - 04:30pm
I'll present a brief overview of the local Langlands programand describe recent joint work with Harrison Chen and David Helm.We establish a categorical or "families" form of the local Langlandscorrespondence: a full embedding of the derived category of representationsof GL_n over a nonarchimedean local field into coherent sheaveson the space of Langlands parameters, as well as an analogousstatement for the ``Iwahori block" for any [split] reductivegroup. The main ingredient is a coherent sheaf version of Springertheory -- an identification of an affine Hecke algebra as theendomorphisms of a coherent sheaf on the loop space of the nilpotentcone -- which combines their K-theoretic realization due to Kazhdan-Lusztigand some derived algebraic geometry.
Location: RLM 9.166

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