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Israel Journal of Mathematics

, Volume 113, Issue 1, pp 61–93 | Cite as

Algebraic modular forms

  • Benedict H. Gross
Article

Abstract

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.

Keywords

Modular Form Division Algebra Open Compact Subgroup Arithmetic Subgroup Central Involution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Magnes Press 1999

Authors and Affiliations

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

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