Rigid local systems with monodromy group the Conway group Co₂

2018/11/14 by Katz, Nicholas M., Rojas-León, Antonio, Tiep, Pham Huu
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.05712

Abstract

We first develop some basic facts about hypergeometric sheaves on the multiplicative group \mathbb G_m in characteristic p >0. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic p>0. One of these, of rank 23 in characteristic p=3, turns out to have the Conway group Co₂, in its irreducible orthogonal representation of degree 23, as its arithmetic and geometric monodromy groups.

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