Supersingular curves via the Shimura--Taniyama method
Number Theory
2025-05-23 v2 Algebraic Geometry
Abstract
For a curve which admits an abelian cover of the projective line branched at three points, we study when its reduction to positive characteristic is supersingular. Using the method of Shimura and Taniyama, we give a complete classification when the genus of the curve is at most 10. The natural density of the set of primes for which this construction yields a supersingular curve is larger than expected.
Keywords
Cite
@article{arxiv.2503.04878,
title = {Supersingular curves via the Shimura--Taniyama method},
author = {Jeremy Booher and Rachel Pries},
journal= {arXiv preprint arXiv:2503.04878},
year = {2025}
}
Comments
14 pages. This is an expanded version of section 4 of arXiv:2410.20262, which we are splitting off into a separate preprint. arXiv admin note: text overlap with arXiv:2410.20262