2023/04/10 by Brian Yang, Yang, Brian
Engineering · Mathematics · #11G10 #11G20 #14H30 #14H40 #14K22 #16Kxx #20C15 (Primary) #20C15 (Secondary) #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2304.04557
openalex publication_date 2023/04/10 · openalex created_date 2023/04/12 · openalex updated_date 2026/07/28
Within the Schottky problem, the study of special subvarieties of the Torelli locus has long been of great interest. We describe a representation-theoretic criterion for a Jacobian variety arising from a G-Galois cover of ℙ1 branched at 3 points to have complex multiplication (CM). For G faithful metacyclic or dicyclic, we classify all such covers with Galois group G, identifying those that have CM. We compute the CM-field and type of Jacobian varieties arising from these covers, applying the representation theory of G over ℚ and ℚ(ζ4). In particular, symplectic irreducible representations of G are afforded by the Jacobian variety in the dicyclic case, giving rise to new examples of CM abelian varieties.