Algebra/Number Theory Seminar
Speaker: Arne Smeets (Université Lille 1)
Title: Logarithmic good reduction, monodromy and the rational volume.
Abstract: Let R be a local ring which is complete for a discrete valuation, with fraction field K and algebraically closed residue field k. Let Xbe a smooth, proper variety over K. Nicaise conjectured that the rational volume of X is equal to the trace of the tame monodromy operator on the ℓ-adic cohomology if X is cohomologically tame. We prove his conjecture for a large class of such varieties: those having logarithmic good reduction.