Trace and Kunneth formulas for singularity categories and applications

2017/10/16 by Toën, Bertrand, Vezzosi, Gabriele
#11F80 #13D09 #14B07 #14F42 #19D23 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1710.05902

Abstract

We present an ℓ-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. Moreover, we prove Künneth 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.

Related

• The ℓ-adic trace formula for dg-categories and Bloch's conductor conjecture
• Motivic and ℓ-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle
• Motivic Realizations of Singularity Categories and Vanishing Cycles
• Traces in monoidal categories
• Applications of (higher) categorical trace I: the definition of AGCat