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.



Modern reference for the theory of correspondences for curves
Griffiths and Harris, *[Principles of Algebraic Geometry](http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471050598.html)*.


See in particular Chapter 2 (*Riemann Surfaces and Algebraic Curves*), Section 5 (*Correspondences*). 


