Holonomy group scheme of an integral curve

Let Y be a projective variety over a field k (of arbitrary characteristic). Assume that the normalization X of Y is such that Xk¯ is normal, k¯ being the algebraic closure of k. We define a notion of strong semistability for vector bundles on Y. We show that a vector bundle on Y is strongly semistable if and only if its pull back to X is strongly semistable and hence it is a tensor category. In case dimY=1, we show that strongly semistable vector bundles on Y form a neutral Tannakian category. We define the holonomy group scheme GY of Y to be the Tannakian group scheme for this category. For a strongly semistable principal G‐bundle EG, we construct a holonomy group scheme. We show that if Y is an integral complex nodal curve, then the holonomy group of a strongly semistable vector bundle on Y is the Zariski closure of the (topological) fundamental group of Y.