Primes of bad reduction for genus 3 CM curves and their exponents on the discriminant (joint work with S. Ionica, P. Kilicer, K. Lauter, A. Manzateanu and C. Vincent)
Heilbronn Number Theory Seminar
27th May 2020, 4:00 pm – 5:00 pm
Let O be an order on a sextic CM field. In order to construct genus 3 curves whose Jacobian has CM by O we need to construct class polynomials, and for doing this we need to control the primes in the discriminant of the curves and their exponents. In previous works I studied the so-called "embedding problem" in order to bound the primes of bad reduction. In the present one we give an algorithm to explicitly compute them and we bound the exponent of those primes in the discriminant for the hyperelliptic case. Several examples will be given.