Inventiones mathematicae

, Volume 195, Issue 1, pp 1–277 | Cite as

The Iwasawa Main Conjectures for GL2

  • Christopher Skinner
  • Eric Urban


We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2).



Both authors gratefully acknowledge their many fruitful conversations with colleagues, especially Ralph Greenberg, Michael Harris, Haruzo Hida, and Andrew Wiles. It also pleasure to thank Xin Wan and the referees for their careful reading of this paper and their helpful comments. The research of the first named author was supported by grants from the National Science Foundation and by a fellowship from the David and Lucile Packard Foundation. The second named author was supported at different times by the CNRS and by grants from the National Science Foundation and by a fellowship from the Guggenheim Foundation.


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Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Institut Mathématiques de JussieuParisFrance
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA

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