Affine Toric Equivalence Relations are Effective

Details Affine Toric Equivalence Relations are Effective Affine Toric Equivalence Relations are Effective

2009-05-29

arxiv.org/abs/0905.4805v2

Mathematics

Algebraic Geometry

v2: substantial revisions - generalized Theorem 3.1, corrected treatment of the general case of Theorem 4.1, removed erroneous

Scientific paper

Any map of schemes $X\to Y$ defines an equivalence relation $R=X\times_Y X\to X\times X$, 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. In special cases, this result is a consequence of the vanishing of the first cohomology group in the Amitsur complex associated to a toric map of toric algebras. We prove more generally the exactness of the Amitsur complex for maps of commutative monoid rings.

Affiliated with

Also associated with

No associations

Rating

Affine Toric Equivalence Relations are Effective does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Affine Toric Equivalence Relations are Effective, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Affine Toric Equivalence Relations are Effective will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-526956