Primes of bad reduction for CM curves of genus 3 and their exponents on the discriminant
Elisa Lorenzo García (Universtiy of Rennes 1)
Abstract: Let O be an order in 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.
(joint work with S. Ionica, P. Kilicer, K. Lauter, A. Manzateanu and C. Vincent)
algebraic geometrynumber theory
Audience: researchers in the topic
Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).
We acknowledge the support of PIMS, NSERC, and SFU.
For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.
We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca
| Organizer: | Katrina Honigs* |
| *contact for this listing |