arXiv:1007.4004 On a conjecture of Deligne from arXiv Front: math.NT by Vladimir Drinfeld Let X be a smooth variety over . Let E be a number field. For each nonarchimedean place of E prime to p consider the set of isomorphism classes of irreducible lisse -sheaves on X with determinant of finite order such that for every closed point x in X the characteristic polynomial of the Frobenius has coefficents in E. We prove that this set does not depend on
The idea is to use a method developed by G.Wiesend to reduce the problem to the case where X is a curve. This case was treated by L. Lafforgue.
nLab page on Independence of l