Honda theory for formal groups of abelian varieties over Q of GL2-type

Yuken Miyasaka, Hirokazu Shinjo

Research output: Contribution to journalReview article

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 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.

Original languageEnglish
Pages (from-to)355-372
Number of pages18
JournalJournal of Mathematical Sciences (Japan)
Volume21
Issue number2
Publication statusPublished - 2014 Jan 1

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Honda theory for formal groups of abelian varieties over Q of GL<sub>2</sub>-type'. Together they form a unique fingerprint.

  • Cite this