Local systems and finite unitary and symplectic groups

Nicholas M. Katz, Pham Huu Tiep

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5 Scopus citations


For powers q of any odd prime p and any integer n≥2, we exhibit explicit local systems, on the affine line A1 in characteristic p>0 if 2|n and on the affine plane A2 if 2∤n, whose geometric monodromy groups are the finite symplectic groups Sp2n(q). When n≥3 is odd, we show that the explicit rigid local systems on the affine line in characteristic p>0 constructed in [11] do have the special unitary groups SUn(q) as their geometric monodromy groups as conjectured therein, and also prove another conjecture of [11] that predicted their arithmetic monodromy groups.

Original languageEnglish (US)
Article number106859
JournalAdvances in Mathematics
StatePublished - Dec 15 2019

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Finite symplectic groups
  • Finite unitary groups
  • Local systems
  • Monodromy groups
  • Weil representations


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