科研之友
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摘要
Any map of schemes X -> Y defines an equivalence relation R = X x(Y) X -> 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 tone equivalence relations always exist in the affine case. In special cases, this result is a consequence of the vanishing of the first cohomology group in the Amitsur complex associated to a tonic map of tone algebras. We prove more generally the exactness of the Amitsur complex for maps of commutative monoid rings.
- 出版日期2010-11
