Let be a strictly local ring complete for a discrete valuation, with fraction field and residue field of characteristic . Let be a smooth, proper variety over . Nicaise conjectured that the rational volume of is equal to the trace of the tame monodromy operator on -adic cohomology if is cohomologically tame. He proved this equality if is a curve. We study his conjecture from the point of view of logarithmic geometry, and prove it for a class of varieties in any dimension: those having logarithmic good reduction.
"Logarithmic good reduction, monodromy and the rational volume." Algebra Number Theory 11 (1) 213 - 233, 2017. https://doi.org/10.2140/ant.2017.11.213