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Original Articles

Evidence for the Dynamical Brauer–Manin Criterion

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References

  • [Amerik 11] E. Amerik. “Existence of Non-Preperiodic Algebraic Points for a Rational Self-Map of Infinite Order.” Math. Res. Lett. 18 (2011), 251–256.
  • [Atiyah and Macdonald 69] M. F. Atiyah and I. G. Macdonald. Introduction to Commutative Algebra. Reading, MA-London-Don Mills, Ont.: Addison-Wesley Publishing Co., 1969. MR0242802 (39 #4129).
  • [Bell et al. 10] J. P. Bell, D. Ghioca, and T. J. Tucker. “The Dynamical Mordell-Lang Problem for étale Maps.” Amer. J. Math. 132: 6 (2010), 1655–1675. MR2766180 (2012a:37202).
  • [Benedetto et al. 13] Robert L. Benedetto, Dragos Ghioca, Benjamin Hutz, Pär Kurlberg, Thomas Scanlon, and Thomas J. Tucker. “Periods of Rational Maps Modulo Primes.” Math. Ann. 355: 2 (2013), 637–660. MR3010142. doi:10.1007/s00208-012-0799-8.
  • [Bosma et al. 97] Wieb Bosma, John Cannon, and Catherine Playoust. “The Magma Algebra System. I. The User Language.” J. Symbolic Comput. 24: 3–4 (1997), 235–265. Computational algebra and number theory (London, 1993). MR1484478. doi:10.1006/jsco.1996.0125.
  • [Fakhruddin 03] Najmuddin Fakhruddin. “Questions on Self Maps of Algebraic Varieties.” J. Ramanujan Math. Soc. 18: 2 (2003), 109–122. MR1995861.
  • [Flajolet and Odlyzko 89] Philippe Flajolet and Andrew M. Odlyzko. “Random Mapping Statistics.” In Advances in Cryptology—EUROCRYPT ’89, Houthalen, 1989. Lecture Notes in Comput. Sci., vol. 434, pp. 329–354. Berlin: Springer, 1990. MR1083961.
  • [Grothendieck 67] A. Grothendieck. “Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes des schémas. IV.” Inst. Hautes Études Sci. Publ. Math. 32 (1967), 361 pp.
  • [Hartshorne 77] Robin Hartshorne. Algebraic Geometry. New York, NY: Springer-Verlag, 1977. Graduate Texts in Mathematics, No. 52. MR0463157 (57 #3116).
  • [Hsia and Silverman 09] Liang-Chung Hsia and Joseph Silverman. “On a Dynamical Brauer-Manin Obstruction.” J. Théor. Nombres Bordeaux 21: 1 (2009), 235–250 (English, with English and French summaries). MR2537714 (2010f:37157).
  • [Pink 04] Richard Pink. “On the Order of the Reduction of a Point on an Abelian Variety.” Math. Ann. 330: 2 (2004), 275–291. MR2089426 (2005g:11101). doi:10.1007/s00208-004-0548-8.
  • [Poonen 06] Bjorn Poonen. “Heuristics for the Brauer-Manin Obstruction for Curves.” Exp. Math. 15: 4 (2006), 415–420. MR2293593 (2008d:11062).
  • [Poonen 14] Bjorn Poonen. “p-Adic Interpolation of Iterated.” Bull. Lond. Math. Soc. 46: 3 (2014), 525–527.
  • [Scharaschkin 99] Victor Scharaschkin. “Local-Global Problems and the Brauer-Manin Obstruction.” Thesis (Ph.D.), University of Michigan, ProQuest LLC, Ann Arbor, MI, 1999. MR2700328.
  • [Silverman and Voloch 09] Joseph H. Silverman and José Felipe Voloch. “A Local-Global Criterion for Dynamics on .” Acta Arith. 137: 3 (2009), 285–294. MR2496466 (2010g:37173). doi:10.4064/aa137-3-8.
  • [Stein 13] W. A. Stein. “Sage Mathematics Software (Version 4.8).” The Sage Development Team. Available at http://www.sagemath.org, 2013.
  • [Tenenbaum and Mendès France 00] Gérald Tenenbaum and Michel Mendès France. The Prime Numbers and Their Distribution. Student Mathematical Library, vol. 6. Providence, RI: American Mathematical Society, 2000. Translated from the 1997 French original by Philip G. Spain. MR1756233 (2001j:11086).

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