Galois Theory and Modular Forms pp 13-37

Part of the Developments in Mathematics book series (DEVM, volume 11)

Semistable Abelian Varieties with Small Division Fields

  • Armand Brumer
  • Kenneth Kramer

Abstract

The conjecture of Shimura-Taniyama-Weil, now proved through the work of Wiles and disciples, is only part of the Langlands program. Based on a comparison of the local factors ([And], [Seri]), it also predicts that the L-series of an abelian surface defined over ℚ should be the L-series of a Hecke eigen cusp form of weight 2 on a suitable group commensurable with Sp4 (ℤ). The only decisive examples are related to lifts of automorphic representations of proper subgroups of Sp4, for example the beautiful work of Yoshida ([Yos], [BSP]).

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Armand Brumer
    • 1
  • Kenneth Kramer
    • 2
  1. 1.Department of MathematicsFordham UniversityBronxUSA
  2. 2.Department of MathematicsQueens College (CUNY)FlushingUSA

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