Trace and Künneth formulas for singularity categories and applications

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.