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 $X$be 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 $\ell$-adic cohomology if $X$ is cohomologically tame. We prove his conjecture for a large class of such varieties: those having logarithmic good reduction.