Nous démontrons l’existence des modèles minimaux globaux pour les endomorphismes de l’espace projectif sur le corps des fractions d’un anneau principal.
We prove the existence of global minimal models for endomorphisms of projective space defined over the field of fractions of a principal ideal domain.
@article{JTNB_2014__26_3_813_0, author = {Petsche, Clayton and Stout, Brian}, title = {Global minimal models for endomorphisms of projective space}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {813--823}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {26}, number = {3}, year = {2014}, doi = {10.5802/jtnb.889}, mrnumber = {3320502}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.889/} }
TY - JOUR AU - Petsche, Clayton AU - Stout, Brian TI - Global minimal models for endomorphisms of projective space JO - Journal de théorie des nombres de Bordeaux PY - 2014 SP - 813 EP - 823 VL - 26 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.889/ DO - 10.5802/jtnb.889 LA - en ID - JTNB_2014__26_3_813_0 ER -
%0 Journal Article %A Petsche, Clayton %A Stout, Brian %T Global minimal models for endomorphisms of projective space %J Journal de théorie des nombres de Bordeaux %D 2014 %P 813-823 %V 26 %N 3 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.889/ %R 10.5802/jtnb.889 %G en %F JTNB_2014__26_3_813_0
Petsche, Clayton; Stout, Brian. Global minimal models for endomorphisms of projective space. Journal de théorie des nombres de Bordeaux, Tome 26 (2014) no. 3, pp. 813-823. doi : 10.5802/jtnb.889. http://www.numdam.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 | Zbl
[2] N. Bruin et A. Molnar, Minimal models for rational functions in a dynamical setting, LMS J. Comp. Math., 15, (2012), 400–417. | MR | Zbl
[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 | Zbl
[4] S. Lang, Algebra, third ed, Graduate Texts in Mathematics, 211, Springer-Verlag, New York, (2002). | MR | Zbl
[5] C. Petsche, Critically separable rational maps in families, Comp. Math., 148, (2012), 6, 1880–1896. | MR
[6] J. H. Silverman, The arithmetic of dynamical systems. Graduate Texts in Mathematics 241, Springer-Verlag, New York, (2007). | MR | Zbl
[7] J. H. Silverman, The arithmetic of elliptic curves, second ed, Graduate Texts in Mathematics, 106, Springer, Dordrecht, (2009). | MR | Zbl
[8] B. Stout, A dynamical Shafarevich theorem for twists of rational morphisms, Preprint (2013), http://arxiv.org/abs/1308.4992 | MR
[9] L. Szpiro et T. J. Tucker, A Shafarevich-Faltings theorem for rational functions, Pure Appl. Math. Q. 4, (2008), 3, 715–728. | MR | Zbl
[10] B. van der Waerden, Modern Algebra Vol. II, Frederick Ungar Publishing Co., New York, (1949). | MR | Zbl
Cité par Sources :