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

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

Building on the recent paper (Blanc et al. preprint, arXiv:1607.03012 ), 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 just an E 2 -algebra. As an application of this trace formula, we propose a strategy of proof...

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Veröffentlicht in:Bollettino della Unione matematica italiana (2008) 2019-03, Vol.12 (1-2), p.3-17
Hauptverfasser: Toën, Bertrand, Vezzosi, Gabriele
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Conductors
Mathematics
Mathematics and Statistics
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Zusammenfassung:Building on the recent paper (Blanc et al. preprint, arXiv:1607.03012 ), 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 just an 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.
ISSN:1972-6724
2198-2759
DOI:10.1007/s40574-018-0166-0