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

Nicholas M. Katz; Pham Huu Tiep

doi:10.1016/j.jpaa.2024.107679

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

Nicholas M. Katz, Pham Huu Tiep

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	American English
Article number	107679
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2024.107679
State	Published - Sep 2024

ASJC Scopus subject areas

Algebra and Number Theory

Keywords

Hypergeometric sheaves
Local systems
Monodromy groups

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10.1016/j.jpaa.2024.107679

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AB - 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.

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KW - Local systems

KW - Monodromy groups

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

Abstract

ASJC Scopus subject areas

Keywords

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