A derived local Langlands correspondence for GL_n

A derived local Langlands correspondence for GL_n

Abstract: We describe joint work with David Ben-Zvi and David Nadler that constructs a version of the local Langlands correspondence that is an equivalence on the level of categories, rather than a bijection between isomorphism classes of objects. More precisely, we show that there is an equivalence between the derived category of smooth representations of GL_n and a certain category of coherent sheaves on a moduli space of Langlands parameters. The proof of this equivalence is essentially a reinterpretation of results of Kazhdan-Lusztig via derived algebraic geometry.