Global minimal models for endomorphisms of projective space

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.

Journal de Théorie des Nombres de Bordeaux (2014)

  • Volume: 26, Issue: 3, page 813-823
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Petsche, Clayton, and Stout, Brian. "Global minimal models for endomorphisms of projective space." Journal de Théorie des Nombres de Bordeaux 26.3 (2014): 813-823. <http://eudml.org/doc/275701>.

@article{Petsche2014,
abstract = {We prove the existence of global minimal models for endomorphisms $\phi :\mathbb\{P\}^N\rightarrow \mathbb\{P\}^N$ of projective space defined over the field of fractions of a principal ideal domain.},
affiliation = {Department of Mathematics Oregon State University Corvallis OR 97331 U.S.A.; Ph.D. Program in Mathematics CUNY Graduate Center 365 Fifth Avenue New York, NY 10016-4309 U.S.A.},
author = {Petsche, Clayton, Stout, Brian},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {12},
number = {3},
pages = {813-823},
publisher = {Société Arithmétique de Bordeaux},
title = {Global minimal models for endomorphisms of projective space},
url = {http://eudml.org/doc/275701},
volume = {26},
year = {2014},
}

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
DA - 2014/12//
PB - Société Arithmétique de Bordeaux
VL - 26
IS - 3
SP - 813
EP - 823
AB - We prove the existence of global minimal models for endomorphisms $\phi :\mathbb{P}^N\rightarrow \mathbb{P}^N$ of projective space defined over the field of fractions of a principal ideal domain.
LA - eng
UR - http://eudml.org/doc/275701
ER -

References

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  7. J. H. Silverman, The arithmetic of elliptic curves, second ed, Graduate Texts in Mathematics, 106, Springer, Dordrecht, (2009). Zbl1194.11005MR2514094
  8. B. Stout, A dynamical Shafarevich theorem for twists of rational morphisms, Preprint (2013), http://arxiv.org/abs/1308.4992 Zbl06360641MR3273498
  9. L. Szpiro et T. J. Tucker, A Shafarevich-Faltings theorem for rational functions, Pure Appl. Math. Q. 4, (2008), 3, 715–728. Zbl1168.14020MR2435841
  10. B. van der Waerden, Modern Algebra Vol. II, Frederick Ungar Publishing Co., New York, (1949). Zbl0039.00902MR29363

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