For hyperelliptic curves over local fields with residue characteristic 2, even-cardinality clusters of roots of f determine loops in the graph of the relatively stable model's special fiber if and only if cluster depth exceeds a computable threshold, with an added formula for 2-rank.
Another proof of the Semistable Reduction Theorem
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abstract
We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a suitable finite extension) we construct a semistable model of $X$ whose normalization with respect to the cover is a semistable model of $Y$.
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Clusters, toric ranks, and 2-ranks of hyperelliptic curves in the wild case
For hyperelliptic curves over local fields with residue characteristic 2, even-cardinality clusters of roots of f determine loops in the graph of the relatively stable model's special fiber if and only if cluster depth exceeds a computable threshold, with an added formula for 2-rank.