Conductors of superelliptic curves [thesis]

Roman Kohls, Universität Ulm
2019
The main object of this thesis are conductors associated to algebraic curves. For a superelliptic curve given by y^n=g(x) we give a decomposition of the conductor exponent at primes p not dividing n in n-1 terms such that the wild part of each term is independent of n and given in terms of the polynomial g. Based on this decomposition, we obtain an upper bound for the conductor exponent in terms of g and n. We provide examples showing that this bound is sharp. As an application to the proven
more » ... on to the proven inequalities, we prove that the conductor exponent of a Picard curve at primes not equal to 2 or 3 is bounded by the valuation of a minimal discriminant of the curve.
doi:10.18725/oparu-22641 fatcat:pckqrcccnzhv3mjgnzug7jmeye