Condition (S+) in ranks 4, 8, and 9

Nicholas M. Katz, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review


Condition (S+), introduced in [17], plays a key role in the study of Kloosterman and hypergeometric l-adic local systems in positive characteristic p. Prior results of [17], [20] establish (S+) for primitive Kloosterman and hypergeometric sheaves, except possibly in ranks 4, 8, and 9. In this paper we study (S+) in these remaining ranks, and completely determine when (S+) does or does not hold.

Original languageEnglish (US)
Article number107679
JournalJournal of Pure and Applied Algebra
Issue number9
StatePublished - Sep 2024

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Hypergeometric sheaves
  • Local systems
  • Monodromy groups


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