### Abstract

Honda proved that two formal groups attached to an elliptic curve E over double-struck Q are strongly isomorphic over double-struck Z, where one of them is obtained from the formal completion along the zero section of the Néron model over double-struck Z and another is obtained from the L-series attached to the l-adic Galois representations on E. In this paper, we generalize his theorem to abelian varieties over double-struck Q of GL_{2}-type. As an application, we give a method to calculate the coefficients of the L-series attached to an algebraic curve over double-struck Q with a Jacobian variety of GL_{2}-type.

Original language | English |
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Pages (from-to) | 355-372 |

Number of pages | 18 |

Journal | Journal of Mathematical Sciences (Japan) |

Volume | 21 |

Issue number | 2 |

Publication status | Published - 2014 Jan 1 |

### Keywords

- Abelian variety of GL-type
- Complex multiplication
- Formal group
- L-series

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Miyasaka, Y., & Shinjo, H. (2014). Honda theory for formal groups of abelian varieties over Q of GL

_{2}-type.*Journal of Mathematical Sciences (Japan)*,*21*(2), 355-372.