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 GL2-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 GL2-type.
|Number of pages||18|
|Journal||Journal of Mathematical Sciences (Japan)|
|Publication status||Published - 2014 Jan 1|
- Abelian variety of GL-type
- Complex multiplication
- Formal group
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