Supersingular curves of genus five for primes congruent to three modulo four

Jeremy Booher, Rachel Pries

Published 2024-10-26Version 1

For every prime number $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. This extends earlier work of Ekedahl and of Harashita, Kudo, and Senda.