Local systems and Suzuki groups

Levent Alpöge, Nicholas M. Katz, Gabriel Navarro, E. A. O’Brien, Pham Huu Tiep

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study geometric monodromy groups Ggeom,Fq of the local systems Fq on the affine line over F2 of rank D=√q/2(q−1), q=22n+1, constructed in N. Katz [Exponential sums, Ree groups and Suzuki groups: conjectures, Exp. Math. 28 (2019), 49-56.]. The main result of the paper shows that Ggeom,Fq is either the Suzuki simple group (2B2(q), or the special linear group SLD. We also show that F8 has geometric monodromy group (2B2(8), and arithmetic monodromy group Aut(2B2(8)) over F2, thus establishing Katz’s Conjecture 2.2 in the above cited paper in the case q=8.

Original languageEnglish (US)
Title of host publicationAmitsur Centennial Symposium, 2021
EditorsAvinoam Mann, Louis H. Rowen, David J. Saltman, Aner Shalev, Lance W. Small, Uzi Vishne
PublisherAmerican Mathematical Society
Pages15-79
Number of pages65
ISBN (Print)9781470475550
DOIs
StatePublished - 2024
EventAmitsur Centennial Symposium, 2021 - Jerusalem, Israel
Duration: Nov 1 2021Nov 4 2021

Publication series

NameContemporary Mathematics
Volume800
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceAmitsur Centennial Symposium, 2021
Country/TerritoryIsrael
CityJerusalem
Period11/1/2111/4/21

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • airy sheaves
  • Local systems
  • monodromy groups
  • Suzuki simple groups

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