Models of curves over discrete valuation rings
Tim Dokchitser
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.
Topics & Concepts
MathematicsDiscrete valuation ringAffine transformationEmbeddingSheafDiscrete valuationValuation (finance)Polygon (computer graphics)Pure mathematicsCohomologyNewton polygonValuation ringRing of integersToroidAlgebraic number fieldDiscrete mathematicsField (mathematics)TelecommunicationsQuantum mechanicsArtificial intelligencePlasmaFrame (networking)PhysicsEconomicsFinanceComputer scienceAlgebraic Geometry and Number TheoryPolynomial and algebraic computationCommutative Algebra and Its Applications