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Discriminants and Artin conductors

Journal article
Authors Dennis Eriksson
Published in Journal Fur Die Reine Und Angewandte Mathematik
Issue 712
Pages 107-121
ISSN 0075-4102
Publication year 2016
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 107-121
Language en
Links dx.doi.org/10.1515/crelle-2014-0022
Keywords arithmetic surfaces, elliptic curves, dual varieties, multiplicities, singularities, formula, Mathematics
Subject categories Mathematics

Abstract

We study questions of multiplicities of discriminants for degenerations coming from projective duality over discrete valuation rings. The main observation is a type of discriminant-different formula in the sense of classical algebraic number theory, and we relate it to Artin conductors via Bloch's conjecture. In the case of discriminants of planar curves we can calculate the different precisely. In general these multiplicities encode topological invariants of the singular fibers and in the case of characteristic p, also wild ramification data in the form of Swan conductors. This builds upon results of T. Saito.

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