Grothendieck's relative point of view is a heuristic applied in certain abstract mathematical situations, with a rough meaning of taking for consideration families of 'objects' explicitly depending on parameters, as the basic field of study, rather than a single such object.
It is named after Alexander Grothendieck, who made extensive use of it in treating foundational aspects of algebraic geometry.
This idea is made formal in the idea of the slice category of objects of C 'above' S. To move from one slice to another requires a base change; from a technical point of view base change becomes a major issue for the whole approach (see for example Beck–Chevalley conditions).
It combines, though, with the use of the Yoneda lemma to replace the 'point' idea with that of treating an object, such as S, as 'as good as' the representable functor it sets up.
The more classical types of Riemann–Roch theorem are recovered in the case where S is a single point (i.e. the final object in the working category C).