Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields

Abstract

We prove the semistable reduction theorem for $\mathcal{E}^{\dag}_K$-valued and $K$-valued overconvergent $F$-isocrystals over $k((t))$-varieties which were introduced by Lazda and P\'{a}l. As an application, we prove the finite dimensionality of $\mathcal{E}^{\dag}_K$-valued rigid cohomology with compact support.