Special Points Arising From Faithful Metacyclic and Dicyclic Galois Covers of the Projective Line

Autor:	Yang, Brian
Rok vydání:	2023
Předmět:	Mathematics - Number Theory 11G20 14H40 14K22 (Primary) 16Kxx 20C15 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Within the Schottky problem, the study of special subvarieties of the Torelli locus has long been of great interest. We present a criterion for a dimension $0$ subvariety of the Torelli locus, arising from a $G$-Galois cover of $\mathbb{P}^1$ branched at $3$ points, to be special. We develop methods to compute the complex multiplication field and type of Jacobian varieties arising from these covers, applying the representation theory of $G$ over $\mathbb{Q}$ and $\mathbb{Q}(\zeta_4)$. We also apply the Shimura-Taniyama formula to compute the Newton polygons of these Jacobians. We classify all the $G$-Galois covers for nonabelian faithful metacyclic groups $G$ and dicyclic groups $G$, identifying those that have complex multiplication. Comment: To be submitted to the Transactions of the American Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.04557 Zobrazit plný text záznamu View this record from Arxiv