Séminaire de Cryptographie

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Garcia Lorenzo

Bad reduction of genus 3 curves with complex multiplication

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes P of M such that the stable reduction of C at P contains three irreducible components of genus 1.