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

  title={The \$\$\ell \$\$ℓ-adic trace formula for dg-categories and Bloch’s conductor conjecture},
  author={Bertrand To{\"e}n and Gabriele Vezzosi},
  journal={Bollettino dell'Unione Matematica Italiana},
  • B. ToënG. Vezzosi
  • Published 28 May 2016
  • Mathematics
  • Bollettino dell'Unione Matematica Italiana
Building on the recent paper (Blanc et al. preprint, arXiv:1607.03012), we present an $$\ell $$ℓ-adic trace formula for smooth and proper dg-categories over a base $$\mathbb {E}_\infty $$E∞-algebra B. We also give a variant when B is just an $$\mathbb {E}_2$$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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