2009/10/20 by Johannes Nicaise, Nicaise, Johannes
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.0910.3812
Section 2 has been written down in more detail
openalex publication_date 2009/10/20 · arxiv created 2011/02/01 · arxiv updated 2011/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove an A'Campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field K. As a first application, we relate the orders of the tame monodromy eigenvalues on the ℓ-adic cohomology of a K-curve to the geometry of a relatively minimal sncd-model, and we show that the semi-stable reduction theorem and Saito's criterion for cohomological tameness are immediate consequences of this result. As a second application, we compute the error term in the trace formula for smooth and proper K-varieties. We see that the validity of the trace formula would imply a partial generalization of Saito's criterion to arbitrary dimension.