Local systems and Suzuki groups

2023/05/04 by Alpoge, L., Katz, N. M., Navarro, G. +2
#20C33 #20D06 #20G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11T23 #Secondary 20C15

paper · doi:10.48550/arxiv.2305.03168

Abstract

We study geometric monodromy groups G_\geo,\sFq of the local systems \sF_q on the affine line over \F₂ of rank D=√(q)(q-1), q=2²ⁿ⁺¹, constructed in \citeKa-ERS. The main result of the paper shows that G_\geo,\sFq is either the Suzuki simple group \tw2 B₂(q), or the special linear group \SL_D. We also show that \sF₈ has geometric monodromy group \tw2B₂(8), and arithmetic monodromy group \Aut(\tw2 B₂(8)) over \F₂, thus establishing \cite[Conjecture 2.2]Ka-ERS in full in the case q=8.

Related

• A rigid local system with monodromy group the big Conway group 2.Co₁\n and two others with monodromy group the Suzuki group 6.Suz
• Rigid local systems and finite general linear groups
• Rigid local systems and alternating groups
• Rigid local systems with monodromy group the Conway group Co₂
• A Rigid Local System with Monodromy Group 2.J₂