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

By Kiran S. Kedlaya. Compositio Mathematica, 2004

96 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5d5e53c3402c2bff508f98a13fe14aeb0da3090f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations (2006, background): “to [12] for a more extensive discussion of the points we only summarize here, including attributions. Notation 5.2.1. Throughout this subsection, we take n= 1, drop λ, and write tfor t 1. Also, as in [16], when we write an interval Iout explicitly, we typically omit the parentheses in the notation A”
Good formal structures for flat meromorphic connections, I: Surfaces (2008, unknown): “becomes distinctly more complicated. We will instead use the valuation-theoretic approach that we introduced in our recent work on the problem of semistable reduction for overconvergent F-isocrystals [5, 6, 7, 8]; a similar approach appears in Temkin’s proof of inseparable local uniformization [17].”
Good formal structures for flat meromorphic connections, II: Excellent schemes (2010, methodology): “is very diﬃcult to classify valuations on schemes of dimension greater than 2. We overcome this diﬃculty using a new idea, drawn from our work on semistable reduction for overconvergent F-isocrystals [22, 23, 24, 26], and from Temkin’s proof of inseparable local uniformization for function ﬁelds in ”