Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne (Chapter III, Section 7) and other references done pretty much in the same way.
On the other hand, there is an analytical proof for the small case of complex algebraic curves (compact Riemann surfaces), which makes use of differential forms, meromorphic functions, residue Theorem and so on.
Since the curve case looks this special, I was wondering if anyone knows of the existence of a more simple algebraic proof of Serre's Duality Theorem in the curve case and can give me references.
Thank you very much in advance.
PS: I already asked my question on math.stackexchange, where no one replied.
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