Abstract
This paper describes a method for computing all F-pure ideals for a given Cartier map of a polynomial ring over a finite field.
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Blickle M.: Test ideals via algebras of p −e-linear maps. J. Algebraic Geom., 22, 49–83 (2013)
Blickle M., Böckle G.: Cartier modules: finiteness results. J. Reine Angew. Math., 661, 85–123 (2011)
Blickle M., Mustaţă M., Smith K. E.: Discreteness and rationality of F-thresholds. Michigan Math. J., 57, 43–61 (2008)
A. F. Boix and M. Katzman FPureAlgorithm.m2: a Macaulay2 package for computing F-pure ideals with respect to principal Cartier algebras, Available at http://atlas.mat.ub.edu/personals/aboix/thesis.html, 2013.
M. Brion and S. Kumar Frobenius splitting methods in geometry and representation theory, volume 231 of Progress in Mathematics, Birkhäuser Boston Inc., Boston, MA, 2005.
D. R. Grayson and M. E. Stillman Macaulay2, a software system for research in algebraic geometry, Available at http://www.math.uiuc.edu/Macaulay2/, 2013.
Katzman M.: Parameter-test-ideals of Cohen-Macaulay rings. Compos. Math., 144, 933–948 (2008)
Katzman M.: A non-finitely generated algebra of Frobenius maps. Proc. Amer. Math. Soc., 138, 2381–2383 (2010)
Katzman M., Schwede K.: An algorithm for computing compatibly Frobenius split subvarieties. J. Symbolic Comput., 47, 996–1008 (2012)
M. Katzman and K. Schwede FSplitting, a Macaulay2 package implementing an algorithm for computing compatibly Frobenius split subvarieties, Available at http://katzman.staff.shef.ac.uk/FSplitting/, 2012.
Schwede K.: Test ideals in non-\({\mathbb{Q}}\) -Gorenstein rings. Trans. Amer. Math. Soc., 363, 5925–5941 (2011)
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A. F. Boix is partially supported by MTM2010-20279-C02-01.
M. Katzman is supported by EPSRC grant EP/I031405/1.
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Boix, A.F., Katzman, M. An algorithm for producing F-pure ideals. Arch. Math. 103, 421–433 (2014). https://doi.org/10.1007/s00013-014-0704-7
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DOI: https://doi.org/10.1007/s00013-014-0704-7