The $\ell$-adic trace formula for dg-categories and Bloch's conductor conjecture

Abstract

Building on recent results by A. Blanc, M. Robalo and the authors, we present an $\ell$-adic trace formula for smooth and proper dg-categories over a base ${\mathbb{E}}_{\infty }$-algebra $B$. We also give a variant when $B$ is only an ${\mathbb{E}}_2$-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.

Research announcement; 15 pages

References in corpus (1)

• Thom-Sebastiani & Duality for Matrix Factorizations

Cited by in corpus (1)

• Motivic Realizations of Singularity Categories and Vanishing Cycles