Q-curves of degree 5 and jacobian surfaces of GL 2 -type

Autor:	Ki Ichiro Hashimoto
Rok vydání:	1999
Předmět:	Cusp (singularity) Discrete mathematics Degree (graph theory) Mathematics::Number Theory General Mathematics Algebraic geometry Type (model theory) Combinatorics Mathematics::Algebraic Geometry Number theory Quartic function Twist Abelian group Mathematics
Zdroj:	manuscripta mathematica. 98:165-182
ISSN:	1432-1785 0025-2611
Popis:	We construct a parametric family {E(±)(s,t,u)} of minimal Q-curves of degree 5 over the quadratic fields Q\(\), and the family {C(s,t,u)} of genus two curves over Q covering E{(+)(s,t,u) whose jacobians are abelian surfaces of GL2-type. We also discuss the modularity for them and the sign change between E{(+)(s,t,u) and its twist E(−)(s,t,u), which correspond by modularity to cusp forms of trivial and non-trivial Neben type characters, respectively. We find in {C(s,t,u)} concrete equations of curves over Q whose jacobians are isogenous over cyclic quartic fields to Shimura's abelian surfaces Af attached to cusp forms of Neben type character of level N= 29, 229, 349, 461, and 509.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::28d6e37dc1387d05fd236d3b5e758592 https://doi.org/10.1007/s002290050133 Zobrazit plný text záznamu Full text from SpringerLink