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should say that yesterday, right before my battery died, I had started a bare minimum at sheaf of rational functions, just so as to complete the corresponding entry at function field analogy – table
What is the relationship to the entry sheaf of meromorphic functions? There, a sheaf is defined by sheafification of the presheaf U↦Γ(U,𝒪X)[Γ(U,𝒮)−1], where “Γ(U,𝒮) consists of only the regular sections of 𝒪X over U, i.e. those elements of Γ(U,𝒪X) which are not zero divisors”.
Note that this definition is a bit unprecise: If by “not zero divisor” it is meant that the elements should not be zero divisors in Γ(U,𝒪X), then 𝒮 fails to be a presheaf. If instead by “not zero divisor” it is meant that the elements should be such that their germs are not zero divisors in the rings 𝒪X,x, then we obtain exactly the definition in sheaf of rational functions.
@Ingo
For reference, the Stacks project has a good treatment. I suspect the current material was taken from PlanetMath.
The stub material I had put in just to make the link work was just taken from Wikipedia. Should be improved.
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