| Résume | We describe joint work (with David Ben-Zvi and David Nadler) that constructs an equivalence between the derived category of smooth representations of $GL_n(Q_p)$ and a certain category of coherent sheaves on the moduli stack of Langlands parameters for $GL_n$. The proof of this equivalence is essentially a reinterpretation of $K$-theoretic results of Kazhdan and Lusztig via derived algebraic geometry. We will also discuss (conjectural) extensions of this work to the modular representation theory of $GL_n$. |
