Automorphic realization of residual Galois representations

Robert Guralnick, Michael Harris, Nicholas M. Katz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We show that it is possible in rather general situations to obtain a finite-dimensional modular representation p of the Galois group of a number field F as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over F, provided one works "potentially." The proof is based on a close study of the monodromy of the Dwork family of Calabi-Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification of irreducible subgroups of finite classical groups with certain sorts of generators.

Original languageEnglish (US)
Pages (from-to)915-937
Number of pages23
JournalJournal of the European Mathematical Society
Issue number4
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Automorphy
  • Galois representations
  • Hypergeometric local systems


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