Models of curves over discrete valuation rings

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 we determine when it is minimal, the global sections of its relative dualizing sheaf, and the tame part of the first étale cohomology of C.