In mathematics, the residue formula says that the sum of the residues of a meromorphic differential form on a smooth proper algebraic curve vanishes.
The residue formula states: A geometric way of proving the theorem is by reducing the theorem to the case when X is the projective line, and proving it by explicit computations in this case, for example in Altman & Kleiman (1970, Ch.
Tate (1968) proves the theorem using a notion of traces for certain endomorphisms of infinite-dimensional vector spaces.
can be expressed in terms of traces of endomorphisms on the fraction field
A more recent exposition along similar lines, using more explicitly the notion of Tate vector spaces, is given by Clausen (2009).