Semistable Higgs bundles and representations of algebraic fundamental groups in mixed characteristics

Abstract. I first introduce the project of Lan-Sheng-Zuo on the construction of representations from semistable Higgs bundle over curves in characteristic p, particularly, the functor from  the category of periodic Higgs bundles to that of representations. Then I show that on a generic curve, the  rank-2 Higgs bundles (L+ L^-1, \theta) with \theta to be an isomorphism is a peoridic Higgs bundle of period 1 (up to 2-torsion line bundles).