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Rank-2 Motivic Local Systems

Abstract

Given a variety X, by Simpson the category of rank-2 motivic local systems over X is equivalent to the category of abelian schemes over X of GL_2-type. I shall talk on a recent progress on constructing rank-2 motivic local systems on the projective line removing four points using $p$-adic nonabelian Hodge theory, the global Langlands correspondence over function field of characteristic p by Drinfeld and Deligne's conjecture on p to \ell companions solved by Abe. This is a joint project with R. Krishnamoorthy and J.B. Yang.