The ℓ-adic trace formula for dg-categories and Bloch's conductor conjecture

2016/05/28 by Toën, B., Vezzosi, G.
#14A22 #32S30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.08941

Abstract

Building on recent results by A. Blanc, M. Robalo and the authors, 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.

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