The classic theory of correspondences between smooth algebraic curves can be found in André Weil's *Foundations of algebraic geometry*. However, this reference works in a pre-modern algebraic geometry way. My question is:

Do you know about a modern reference for the theory of correspondences for smooth complete algebraic curves over a field?

There are modern references for the general theory of correspondences, but they require Serre's Tor-formula and all modern intersection theory machinery. I am looking for something that addresses the specific case of correspondences between smooth algebraic curves, and therefore that does not rely on unnecessary general machinery.