Proves semistable reduction for E^dag_K-valued and K-valued overconvergent F-isocrystals on k((t))-varieties, implying finite-dimensionality of compactly supported rigid cohomology.
Arithmetic -modules over Laurent series fields: absolute case , arXiv:2103.10362, (2021)
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Constructs p-adic weight spectral sequence for strictly semi-stable schemes over k[[t]] via arithmetic D-modules, with E1 terms from rigid cohomologies of closed fiber components and conjectural E∞ from nearby cycles over the bounded Robba ring.
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Semistable Reduction Theorem for Overconvergent $F$-isocrystals over Laurent Series Fields
Proves semistable reduction for E^dag_K-valued and K-valued overconvergent F-isocrystals on k((t))-varieties, implying finite-dimensionality of compactly supported rigid cohomology.