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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Cartier modules on toric varieties
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by Jen-Chieh Hsiao, Karl Schwede and Wenliang Zhang PDF
Trans. Amer. Math. Soc. 366 (2014), 1773-1795 Request permission


Assume that $X$ is an affine toric variety of characteristic $p > 0$. Let $\Delta$ be an effective toric $\mathbb {Q}$-divisor such that $K_X+\Delta$ is $\mathbb {Q}$-Cartier with index not divisible by $p$ and let $\phi _{\Delta }:F^e_*\mathscr {O}_X\to \mathscr {O}_X$ be the toric map corresponding to $\Delta$. We identify all ideals $I$ of $\mathscr {O}_X$ with $\phi _{\Delta }(F^e_* I)=I$ combinatorially and also in terms of a log resolution (giving us a version of these ideals which can be defined in characteristic zero). Moreover, given a toric ideal $\mathfrak {a}$, we identify all ideals $I$ fixed by the Cartier algebra generated by $\phi _{\Delta }$ and $\mathfrak {a}$; this answers a question by Manuel Blickle in the toric setting.
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Additional Information
  • Jen-Chieh Hsiao
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Address at time of publication: Department of Mathematics, National Cheng Kung University, No. 1 University Road, Tainan 701, Taiwan R.O.C.
  • Email:,
  • Karl Schwede
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 773868
  • Email:
  • Wenliang Zhang
  • Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
  • MR Author ID: 805625
  • Email:
  • Received by editor(s): August 18, 2011
  • Received by editor(s) in revised form: April 10, 2012
  • Published electronically: November 25, 2013
  • Additional Notes: The first author was partially supported by the NSF grant DMS #0901123
    This research was initiated at the Commutative Algebra MRC held in June 2010. Support for this meeting was provided by the NSF and AMS
    The second author was supported by an NSF postdoctoral fellowship and also by NSF grant DMS #1064485
    The third author was partially supported by the NSF grant DMS #1068946.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 1773-1795
  • MSC (2010): Primary 14M25, 13A35, 14F18, 14B05
  • DOI:
  • MathSciNet review: 3152712