Affine Toric Equivalence Relations are Effective
نویسنده
چکیده
Any map of schemes X → Y defines an equivalence relation R = X ×Y X → X × X, the relation of ”being in the same fiber”. We have shown elsewhere that not every equivalence relation has this form, even if it is assumed to be finite. By contrast, we prove here that every toric equivalence relation on an affine toric variety does come from a morphism and that quotients by finite toric equivalence relations always exist in the affine case. The techniques we develop also allow us to prove the exactness of the Amitsur complex associated to a map of monoidal algebras.
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