$\ell$-independence of the trace of local monodromy in a relative case

Abstract

For a family of varieties, we prove that the alternating sum of the traces of "local" monodromy acting on the $\ell$-adic étale cohomology groups of the generic fiber is an integer which is independent of $\ell$.

27 pages, with an appendix by Qing Lu and Weizhe Zheng