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arXiv · 1807.00025

Models of curves over DVRs

Tim Dokchitser
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Abstract

Let C be a smooth projective curve over a discretely valued field K, defined by an affine equation f(x,y)=0. We construct a model of C over the ring of integers of K using a toroidal embedding associated to the Newton polygon of f. We show that under 'generic' conditions it is regular with normal crossings, and determine when it is minimal, the global sections of its relative dualising sheaf, and the tame part of the first etale cohomology of C.

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Tim Dokchitser. 2018-06-29. Models of curves over DVRs. https://doi.org/10.1215/00127094-2020-0079

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