The \(\ell \)-adic trace formula for dg-categories and Bloch’s conductor conjecture. (English) Zbl 1439.14016
Summary: Building on the recent paper [A. Blanc et al., J. Éc. Polytech., Math. 5, 651–747 (2018; Zbl 1423.14151)], 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 just 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.
MSC:
| 14A22 | Noncommutative algebraic geometry |
| 14F08 | Derived categories of sheaves, dg categories, and related constructions in algebraic geometry |
| 14F20 | Étale and other Grothendieck topologies and (co)homologies |
| 16E45 | Differential graded algebras and applications (associative algebraic aspects) |
| 18G35 | Chain complexes (category-theoretic aspects), dg categories |
Citations:
Zbl 1423.14151References:
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