Models of curves over DVRs

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.

39 pages, minor changes

References in corpus (1)

• The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf

Cited by in corpus (5)

• Models and Integral Differentials of Hyperelliptic Curves
• Three-Torsion Subgroups and Wild Conductor Exponents of Plane Quartics
• Superelliptic curves with large Galois images
• Computing Euler factors of genus 2 curves at odd primes of almost good reduction
• Jumps of Jacobians via orthogonal canonical forms