Research Article

An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps

Volume: 49 Number: 5 October 6, 2020
EN

An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps

Abstract

In this paper, we introduce an explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps which recovers the correspondence given by R. Y. Sharp and Y. Yoshino, and the correspondence given by M. Blickle and G. Böckle.

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Keywords

References

  1. [1] M. Blickle and G. Böckle, Cartier modules: finiteness results, J. Reine Angew. Math. 661, 85-123, 2011.
  2. [2] M. Blickle and K. Schwede, $p^{-1}$-linear maps in algebra and geometry, in: Comm. Algebra, 123–205, Springer, New York, 2013.
  3. [3] M.P. Brodmann and R.Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Second Ed., Cambridge University Press, 2013.
  4. [4] S. Iyengar, G.J. Leuschke, A. Leykin, C. Miller, E. Miller, A.K. Singh, and U.Walther, Twenty-Four Hours of Local Cohomology, American Mathematical Society, 2007.
  5. [5] M. Katzman, Parameter test ideals of Cohen Macaulay rings, Compos. Math. 144 (4), 933–948, 2008.
  6. [6] M. Katzman and W. Zhang, Annihilators of Artinian modules compatible with a Frobenius map, J. Symbolic Comput. 60, 29-46, 2014.
  7. [7] G. Lyubeznik, F-modules: applications to local cohomology and D-modules in characteristic $p > 0$, J. Reine Angew. Math. 491, 65–130, 1997.
  8. [8] R.Y. Sharp and Y. Yoshino, Right and left modules over the Frobenius skew polynomial ring in the F-finite case, Math. Proc. Cambridge Philos. Soc. 150 (3), 419-438, 2011.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

October 6, 2020

Submission Date

May 2, 2019

Acceptance Date

December 2, 2019

Published in Issue

Year 2020 Volume: 49 Number: 5

APA
Yesil, M. (2020). An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps. Hacettepe Journal of Mathematics and Statistics, 49(5), 1625-1634. https://doi.org/10.15672/hujms.559956
AMA
1.Yesil M. An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps. Hacettepe Journal of Mathematics and Statistics. 2020;49(5):1625-1634. doi:10.15672/hujms.559956
Chicago
Yesil, Mehmet. 2020. “An Explicit Version of the Correspondence Between Noetherian Modules With Cartier Maps and Artinian Modules With Frobenius Maps”. Hacettepe Journal of Mathematics and Statistics 49 (5): 1625-34. https://doi.org/10.15672/hujms.559956.
EndNote
Yesil M (October 1, 2020) An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps. Hacettepe Journal of Mathematics and Statistics 49 5 1625–1634.
IEEE
[1]M. Yesil, “An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, pp. 1625–1634, Oct. 2020, doi: 10.15672/hujms.559956.
ISNAD
Yesil, Mehmet. “An Explicit Version of the Correspondence Between Noetherian Modules With Cartier Maps and Artinian Modules With Frobenius Maps”. Hacettepe Journal of Mathematics and Statistics 49/5 (October 1, 2020): 1625-1634. https://doi.org/10.15672/hujms.559956.
JAMA
1.Yesil M. An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps. Hacettepe Journal of Mathematics and Statistics. 2020;49:1625–1634.
MLA
Yesil, Mehmet. “An Explicit Version of the Correspondence Between Noetherian Modules With Cartier Maps and Artinian Modules With Frobenius Maps”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, Oct. 2020, pp. 1625-34, doi:10.15672/hujms.559956.
Vancouver
1.Mehmet Yesil. An explicit version of the correspondence between Noetherian modules with Cartier maps and Artinian modules with Frobenius maps. Hacettepe Journal of Mathematics and Statistics. 2020 Oct. 1;49(5):1625-34. doi:10.15672/hujms.559956