Revista de la
Unión Matemática Argentina
A Clemens–Schmid type exact sequence over a local basis
Genaro Hernandez-Mada
Volume 63, no. 1 (2022), pp. 281–292

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Let $k$ be a finite field of characteristic $p$ and let $X \rightarrow \operatorname{Spec} k[[t]]$ 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.