Semistable reduction for overconvergent F -isocrystals, II: A valuation-theoretic approach
نویسنده
چکیده
We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann-Zariski space associated to the function field of a variety. We also make some initial reductions, which allow attention to be focused on valuations of height 1 and transcendence degree 0.
منابع مشابه
Semistable reduction for overconvergent F -isocrystals, IV: Refining the local approach
We refine the local approach, introduced in a previous paper, to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. This approach involves formulating a semistable reduction problem which is local on a valuation space (ZariskiRiemann space); here we show that local semistable reduction can it...
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