Rank 2 local systems and abelian varieties
-- Raju Krishnamoorthy, January 25, 2019

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Let X/k be a smooth variety over a finite field. Motivated by work of Corlette-Simpson over the complex numbers, we formulate a conjecture that certain rank 2 local systems on X come from families of abelian varieties. After an introduction to l/p-adic companions, we explain how the existence of a complete set of p-adic companions can be used to approach the conjecture. This is joint work with A. Pál.