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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Affine toric equivalence relations are effective
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by Claudiu Raicu PDF
Proc. Amer. Math. Soc. 138 (2010), 3835-3847 Request permission


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.
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Additional Information
  • Claudiu Raicu
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840 – and – Institute of Mathematics “Simion Stoilow” of the Romanian Academy, RO-014700 Bucharest, Romania
  • MR Author ID: 909516
  • Email:
  • Received by editor(s): September 24, 2009
  • Received by editor(s) in revised form: January 30, 2010
  • Published electronically: May 24, 2010
  • Communicated by: Bernd Ulrich
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3835-3847
  • MSC (2010): Primary 14A15, 14L30
  • DOI:
  • MathSciNet review: 2679607