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Trace and Künneth formulas for singularity categories and applications
Published online by Cambridge University Press: 03 June 2022
Abstract
We present an $\ell$-adic trace formula for saturated and admissible dg-categories over a base monoidal differential graded (dg)-category. Moreover, we prove Künneth formulas for dg-category of singularities and for inertia-invariant vanishing cycles. As an application, we prove a categorical version of Bloch's conductor conjecture (originally stated by Spencer Bloch in 1985), under the additional hypothesis that the monodromy action of the inertia group is unipotent.
MSC classification
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- Research Article
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- © 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence
Footnotes
BT is partially supported by ERC-2016-ADG-741501 and ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.
References
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