We give an algebraic approach to the study of Hitchin pairs and prove the
tensor product theorem for Higgs semistable Hitchin pairs over smooth
projective curves defined over algebraically closed fields k of
characteristic 0 and characteristic p, with p satisfying some natural
bounds. We also prove the corresponding theorem for polystable bundles.Comment: To appear in Annales de l'Institut Fourier, Volume 61 (2011