Honda Theory for Formal Groups of Abelian Varieties over $\mathbb Q$ of $\mathbf GL_{2}$-Type | 東京大学大学院数理科学研究科理学部数学科

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Honda Theory for Formal Groups of Abelian Varieties over $\mathbb Q$ of $\mathbf GL_{2}$ -Type

J. Math. Sci. Univ. Tokyo
Vol. 21 (2014), No. 2, Page 355–372.

Miyasaka, Yuken ; Shinjo, Hirokazu
Honda Theory for Formal Groups of Abelian Varieties over $\mathbb Q$ of $\mathbf GL_{2}$ -Type
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
Honda proved that two formal groups attached to an elliptic curve

$E$ over

$\mathbb Q$ are strongly isomorphic over

$\mathbb Z$ , where one of them is obtained from the formal completion along the zero section of the Néron model over

$\mathbb Z$ 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

$\mathbb Q$ of

$\mathbf GL_{2}$ -type. As an application, we give a method to calculate the coefficients of the L-series attached to an algebraic curve over

$\mathbb Q$ with a Jacobian variety of

$\mathbf GL_{2}$ -type.

Keywords: Formal group, abelian variety of

$\mathbf GL_{2}$ -type, complex multiplication,

$\mathbb L$ -series.

Mathematics Subject Classification (2010): 11G10, 14K22.

Mathematical Reviews Number: MR3288812

Received: 2014-02-28

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Journal of Mathematical Sciences
- Vol. 31 (2024)
  No.1-No.2
- Vol. 30 (2023)
  No.1-No.2-No.3
- Vol. 29 (2022)
  No.1-No.2-No.3
- Vol. 28 (2021)
  No.1-No.2-No.3-No.4
- Vol. 27 (2020)
  No.1
- Vol. 26 (2019)
  No.1-No.2-No.3
- Vol. 25 (2018)
  No.1-No.2
- Vol. 24 (2017)
  No.1-No.2-No.3
- Vol. 23 (2016)
  No.1-No.2-No.3-No.4
- Vol. 22 (2015)
  No.1-No.2-No.3-No.4
- Vol. 21 (2014)
  No.1-No.2
- Vol. 20 (2013)
  No.1-No.2-No.3-No.4
- Vol. 19 (2012)
  No.1-No.2-No.3-No.4
- Vol. 18 (2011)
  No.1-No.2-No.3-No.4
- Vol. 17 (2010)
  No.1-No.2-No.3-No.4
- Vol. 16 (2009)
  No.1-No.2-No.3-No.4
- Vol. 15 (2008)
  No.1-No.2-No.3-No.4
- Vol. 14 (2007)
  No.1-No.2-No.3-No.4
- Vol. 13 (2006)
  No.1-No.2-No.3-No.4
- Vol. 12 (2005)
  No.1-No.2-No.3-No.4
- Vol. 11 (2004)
  No.1-No.2-No.3-No.4
- Vol. 10 (2003)
  No.1-No.2-No.3-No.4
- Vol. 9 (2002)
  No.1-No.2-No.3-No.4
- Vol. 8 (2001)
  No.1-No.2-No.3-No.4
- Vol. 7 (2000)
  No.1-No.2-No.3-No.4
- Vol. 6 (1999)
  No.1-No.2-No.3-No.4
- Vol. 5 (1998)
  No.1-No.2-No.3-No.4
- Vol. 4 (1997)
  No.1-No.2-No.3
- Vol. 3 (1996)
  No.1-No.2-No.3
- Vol. 2 (1995)
  No.1-No.2-No.3
- Vol. 1 (1994)
  No.1-No.2-No.3

Honda Theory for Formal Groups of Abelian Varieties over Q\mathbb Q of GL2\mathbf GL_{2}-Type

Honda Theory for Formal Groups of Abelian Varieties over $\mathbb Q$ of $\mathbf GL_{2}$ -Type