Computing $L$-functions and semistable reduction of superelliptic curves
Authors:
- Irene I. BouwIBIrene I. Bouw
- Stefan WewersSWStefan Wewers
Preprint
Abstract
We give an explicit description of the stable reduction of superelliptic curves of the form $y^n=f(x)$ at primes $\p$ whose residue characteristic is prime to the exponent $n$. We then use this description to compute the local $L$-factor of the curve and the exponent of conductor at $\p$.
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This publication has 9 references indexed in Scilit:
- Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curvesCompositio Mathematica, 2006
- Computing Special Values of MotivicL-FunctionsExperimental Mathematics, 2004
- Models of Curves and Finite CoversCompositio Mathematica, 1999
- Conductor, discriminant, and the Noether formula of arithmetic surfacesDuke Mathematical Journal, 1988
- Stable n-pointed trees of projective linesIndagationes Mathematicae, 1988
- The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$MATHEMATICA SCANDINAVICA, 1983
- On the Kodaira dimension of the moduli space of curvesInventiones Mathematicae, 1982
- The irreducibility of the space of curves of given genusPublications mathématiques de l'IHÉS, 1969
- Good Reduction of Abelian VarietiesAnnals of Mathematics, 1968