A Clemens–Schmid type exact sequence over a local basis

Abstract

. Let k be a finite field of characteristic p and let X → Spec k [[ t ]] be a semistable family of varieties over k . We prove that there exists a Clemens– Schmid type exact sequence for this family. We do this by constructing a larger family defined over a smooth curve and using a Clemens–Schmid exact sequence in characteristic p for this new family.