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Session 2. Algebraic Geometry
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Computing \(L\)-functions of superelliptic curves |
Irene I. Bouw, Ulm University, Germany
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The talk is based on the joint work with Stefan Wewers
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In this talk we discuss an approach for computing the
\(L\)-functions of a curve via stable reduction. We focus on
superelliptic curves \(Y\) defined over a number field, which are
given by an equation \(y^n=f(x)\). We compute the stable reduction
of \(Y\) at primes whose residue characteristic is prime to
\(n\). We then use this information to compute the local
\(L\)-factor and the exponent of the conductor at \(p\).
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