Geometric local systems on the projective line minus four points

2023/05/18 by Yeuk Hay Joshua Lam, Daniel Litt, Lam, Yeuk Hay Joshua +1 · 1 voice
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2305.11314

Abstract

Let J(m) be an m× m Jordan block with eigenvalue 1. For λ∈ ℂ∖\0,1\, we explicitly construct all rank 2 local systems of geometric origin on ℙ¹∖\0,1,λ, ∞\, with local monodromy conjugate to J(2) at 0,1,λ and conjugate to -J(2) at ∞. The construction relies on Katz's middle convolution operation. We use our construction to prove two conjectures of Sun-Yang-Zuo (one of which was proven earlier by Lin-Sheng-Wang; the other was proven independently from us by Yang-Zuo).

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