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arXiv · 1710.05902

Trace and Kunneth formulas for singularity categories and applications

Bertrand Toën·Gabriele Vezzosi
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Abstract

We present an $\ell$-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove K\"unneth formulas for dg-category of singularities, and for inertia-invariant vanishing cycles. As an application, we prove a version of Bloch's Conductor Conjecture (stated by Spencer Bloch in 1985), under the additional hypothesis that the monodromy action of the inertia group is unipotent.

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Bertrand Toën, Gabriele Vezzosi. 2017-10-16. Trace and Kunneth formulas for singularity categories and applications. https://arxiv.org/abs/1710.05902

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