Computing the Weil representation of a superelliptic curve.

We study the Weil representation ρ of a curve over a p -adic field with potential reduction of compact type. We show that ρ can be reconstructed from its stable reduction. For superelliptic curves of the form y n = f (x) at primes p whose residue characteristic is prime to the exponent n we make this explicit. [ABSTRACT FROM AUTHOR]