  We prove formulas for the cohomology and the extension groups of tautological
bundles on punctual Quot schemes over complex smooth projective curves. As a
corollary, we show that the tautological bundle determines the isomorphism
class of the original vector bundle on the curve. We also give a vanishing
result for the push-forward along the Quot--Chow morphism of tensor and wedge
products of duals of tautological bundles.
