Global minimal models for endomorphisms of projective space
Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 3, pp. 813-823.

We prove the existence of global minimal models for endomorphisms φ: N N of projective space defined over the field of fractions of a principal ideal domain.

Nous démontrons l’existence des modèles minimaux globaux pour les endomorphismes φ: N N de l’espace projectif sur le corps des fractions d’un anneau principal.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.889
Clayton Petsche 1; Brian Stout 2

1 Department of Mathematics Oregon State University Corvallis OR 97331 U.S.A.
2 Ph.D. Program in Mathematics CUNY Graduate Center 365 Fifth Avenue New York, NY 10016-4309 U.S.A.
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Clayton Petsche; Brian Stout. Global minimal models for endomorphisms of projective space. Journal de Théorie des Nombres de Bordeaux, Volume 26 (2014) no. 3, pp. 813-823. doi : 10.5802/jtnb.889. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.889/

[1] A. Borel, Some finiteness properties of adele groups over number fields, Inst. Hautes Études Sci. Publ. Math., 16, (1963), 5–30. | Numdam | MR: 202718 | Zbl: 0135.08902

[2] N. Bruin et A. Molnar, Minimal models for rational functions in a dynamical setting, LMS J. Comp. Math., 15, (2012), 400–417. | MR: 3015733 | Zbl: 1300.37051

[3] C. C. Cheng, J. H. McKay et S. S. Wang, A chain rule for multivariable resultants, Proc. Amer. Math. Soc., 123, (1995), 4, 1037–1047. | MR: 1227515 | Zbl: 0845.12001

[4] S. Lang, Algebra, third ed, Graduate Texts in Mathematics, 211, Springer-Verlag, New York, (2002). | MR: 1878556 | Zbl: 0984.00001

[5] C. Petsche, Critically separable rational maps in families, Comp. Math., 148, (2012), 6, 1880–1896. | MR: 2999309

[6] J. H. Silverman, The arithmetic of dynamical systems. Graduate Texts in Mathematics 241, Springer-Verlag, New York, (2007). | MR: 2316407 | Zbl: 1130.37001

[7] J. H. Silverman, The arithmetic of elliptic curves, second ed, Graduate Texts in Mathematics, 106, Springer, Dordrecht, (2009). | MR: 2514094 | Zbl: 1194.11005

[8] B. Stout, A dynamical Shafarevich theorem for twists of rational morphisms, Preprint (2013), http://arxiv.org/abs/1308.4992 | MR: 3273498

[9] L. Szpiro et T. J. Tucker, A Shafarevich-Faltings theorem for rational functions, Pure Appl. Math. Q. 4, (2008), 3, 715–728. | MR: 2435841 | Zbl: 1168.14020

[10] B. van der Waerden, Modern Algebra Vol. II, Frederick Ungar Publishing Co., New York, (1949). | MR: 29363 | Zbl: 0039.00902

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