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

Yıl 2020, Cilt: 49 Sayı: 5, 1625 - 1634, 06.10.2020

Mehmet Yesil

https://doi.org/10.15672/hujms.559956

Öz

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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Anahtar Kelimeler

Cartier maps, Frobenius maps, Noetherian modules, Artinian modules

Kaynakça

• [1] M. Blickle and G. Böckle, Cartier modules: finiteness results, J. Reine Angew. Math. 661, 85-123, 2011.
• [2] M. Blickle and K. Schwede, $p^{-1}$-linear maps in algebra and geometry, in: Comm. Algebra, 123–205, Springer, New York, 2013.
• [3] M.P. Brodmann and R.Y. Sharp, Local Cohomology: An Algebraic Introduction with Geometric Applications, Second Ed., Cambridge University Press, 2013.
• [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] M. Katzman, Parameter test ideals of Cohen Macaulay rings, Compos. Math. 144 (4), 933–948, 2008.
• [6] M. Katzman and W. Zhang, Annihilators of Artinian modules compatible with a Frobenius map, J. Symbolic Comput. 60, 29-46, 2014.
• [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] 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.