M ay 2 01 6 The ladic trace formula for dg-categories and Bloch ’ s conductor conjecture

Building on [BRTV], we present an l-adic trace formula for smooth and proper dg-categories over a base E∞-algebra B. We also give a variant when B is only an E2-algebra. As an application of this trace formula, we propose a strategy of proof of Bloch’s conductor conjecture. This is a research announcement and detailed proofs will appear elsewhere.