Israel Journal of Mathematics

, Volume 113, Issue 1, pp 61–93

Algebraic modular forms

  • Benedict H. Gross

DOI: 10.1007/BF02780173

Cite this article as:
Gross, B.H. Isr. J. Math. (1999) 113: 61. doi:10.1007/BF02780173


In this paper, we develop an algebraic theory of modular forms, for connected, reductive groupsG overQ with the property that every arithmetic subgroup Γ ofG(Q) is finite. This theory includes our previous work [15] on semi-simple groupsG withG(R) compact, as well as the theory of algebraic Hecke characters for Serre tori [20]. The theory of algebraic modular forms leads to a workable theory of modular forms (modp), which we hope can be used to parameterize odd modular Galois representations.

The theory developed here was inspired by a letter of Serre to Tate in 1987, which has appeared recently [21]. I want to thank Serre for sending me a copy of this letter, and for many helpful discussions on the topic.

Copyright information

© The Magnes Press 1999

Authors and Affiliations

  • Benedict H. Gross
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA