Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve

Let Nc be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree, over a smooth projective curve C. This paper identifies the algebraic cohomology ring HA∗(Nc), i.e. the subring of the rational cohomology ring H∗(Nc; Q) spanned by the fundamental classes of algebraic cycles, in terms of the algebraic cohomology ring of the Jacobian Jc.