Generalized Legendre curves and quaternionic multiplication
| Autor: | Alyson Deines, Ling Long, Fang-Ting Tu, Jenny G. Fuselier, Holly Swisher |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
Endomorphism Mathematics - Number Theory Quaternion algebra 010102 general mathematics Complex multiplication Abelian extension Elementary abelian group 01 natural sciences 010101 applied mathematics Algebra Abelian variety of CM-type FOS: Mathematics Number Theory (math.NT) 0101 mathematics Abelian group 33C05 11G10 11F80 Mathematics Arithmetic of abelian varieties |
| Zdroj: | Journal of Number Theory. 161:175-203 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2015.04.019 |
| Popis: | This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of 2-dimensional abelian varieties of this kind, we determine when the endomorphism algebra of each fiber defined over the algebraic closure of Q contains a quaternion algebra. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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