Exponential Sums, Ree Groups and Suzuki Groups: Conjectures

Abstract

Inspired by work of Gross, we exhibit rigid local systems on the affine line whose monodromy groups we conjecture to be the Suzuki and Ree groups, in characteristics 2 and 3 respectively. We give some numerical evidence for these conjectures.

Keywords:

• monodromy
• local system
• Ree group
• Suzuki group

2010 AMS SUBJECT CLASSIFICATION:

• 11T23
• 20C33