Geometric criteria for tame ramification

Johannes Nicaise

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arXiv · 0910.3812

Geometric criteria for tame ramification

Johannes Nicaise

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Abstract

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 $\ell$-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.

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BibTeX RIS

Johannes Nicaise. 2011-02-01. Geometric criteria for tame ramification. https://arxiv.org/abs/0910.3812

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