Let k be an algebraically closed field of characteristic p > 3 and S be a smooth projective surface over k with k-rational point x. For n ≥ 2, let S [n] denote the Hilbert scheme of n points on S. In this note, we compute the fundamental group scheme π alg (S [n] , ñx) defined by the Tannakian category of stratified bundles on S [n] .
Stratified bundlesLet k be a field of characteristic p and X be a noetherian scheme over k. Stratified bundles on X are sequences of coherent sheaves on X satisfying infinite Frobenius descent. More precisely, the category of stratified bundles on X, denoted S(X), consists of) Let f : Y → X be a morphism and (E i , α i ) be a stratified bundle on X. Then we can define the pullback along f , denoted f * (E i , α i ), as consisting of the sequence of O Y coherent sheaves f * E i and isomorphisms are given by the composite maps