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1 results

  • Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions

  • Kiran S. Kedlaya
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 5 / September 2007
    Published online by Cambridge University Press:
    20 September 2007, pp. 1164-1212
    Print publication:
    September 2007
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  • Let $X$ be a smooth variety over a field $k$ of characteristic $p>0$, and let $\mathcal{E}$ be an overconvergent isocrystal on $X$. We establish a criterion for the existence of a ‘canonical logarithmic extension’ of $\mathcal{E}$ to a smooth compactification $\overline{X}$ of $X$ whose complement is a strict normal crossings divisor. We also obtain some related results, including a form of Zariski–Nagata purity for isocrystals.