We present an l-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove Kunneth 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.
Trace and Künneth formulas for singularity categories and applications / Gabriele Vezzosi. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - STAMPA. - 158:(2022), pp. 483-528. [10.1112/S0010437X22007424]
Trace and Künneth formulas for singularity categories and applications
Gabriele Vezzosi
2022
Abstract
We present an l-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove Kunneth 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.File | Dimensione | Formato | |
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