Determining the primes of bad reduction of CM curves of genus 3
Kristin Lauter
Meta
https://ai.meta.com/people/786716476205590/kristin-e-lauter/
Date(s) : 30/04/2026 iCal
11h00 - 12h00
Bounding and computing the primes of bad reduction for CM curves of genus > 1 is an interesting problem, both for its applications to practical algorithms for generating secure curves for use in cryptography, and for creating catalogues analogous to Cremona’s tables for elliptic curves.
In this talk we explain a method and algorithm for determining the primes of bad reduction for genus 3 CM curves. The proof relies on defining and studying an embedding problem in genus 3 analogous to the embedding problem defined by Goren-Lauter in genus 2. In genus 2 case, an exact formula for the primes of bad reduction was given in the work of Lauter-Viray, but in genus 3 we give instead an algorithm to compute the primes.
This talk is joint work with: Sorina Ionica, Pinar Kiliçer, Kristin Lauter, Elisa Lorenzo García, Adelina Mânzăţeanu, Christelle Vincent
Emplacement
I2M Luminy - TPR2, Amphithéâtre Herbrand 130-134 (1er étage)
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