The field of definition for dynamical systems on 1

Joseph H. Silverman

Compositio Mathematica (1995)

  • Volume: 98, Issue: 3, page 269-304
  • ISSN: 0010-437X

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Silverman, Joseph H.. "The field of definition for dynamical systems on $\mathbb {P}^1$." Compositio Mathematica 98.3 (1995): 269-304. <http://eudml.org/doc/90404>.

@article{Silverman1995,
author = {Silverman, Joseph H.},
journal = {Compositio Mathematica},
keywords = {dynamical systems; field of definition; field of moduli},
language = {eng},
number = {3},
pages = {269-304},
publisher = {Kluwer Academic Publishers},
title = {The field of definition for dynamical systems on $\mathbb \{P\}^1$},
url = {http://eudml.org/doc/90404},
volume = {98},
year = {1995},
}

TY - JOUR
AU - Silverman, Joseph H.
TI - The field of definition for dynamical systems on $\mathbb {P}^1$
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 98
IS - 3
SP - 269
EP - 304
LA - eng
KW - dynamical systems; field of definition; field of moduli
UR - http://eudml.org/doc/90404
ER -

References

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  9. 9 Lang, S.: Fundamentals of Diophantine Geometry, Springer-Verlag, New York, 1983. Zbl0528.14013MR715605
  10. 10 Morton, P.: Arithmetic properties of periodic points of quadratic maps, Acat Arith.LXII (1992), 343-372. Zbl0767.11016MR1199627
  11. 11 Morton, P. and Silverman, J.H.: Periodic points, multiplicities, and dynamical units, J. Reine ang. Math. (to appear). Zbl0813.11059MR1324210
  12. 12 Morton, P. and Silverman, J.H.: Rational periodic points of rational functions, Inter. Math. Research Notices2 (1994), 97-109. Zbl0819.11045MR1264933
  13. 13 Mumford, D. and Fogarty, J.: Geometric Invariant Theory2nd ed., Springer-Verlag, Berlin, 1982. Zbl0504.14008MR719371
  14. 14 Narkiewicz, W.: Polynomial cycles in algebraic number fields, Colloquium Math.58 (1989), 151-155. Zbl0703.12002MR1028168
  15. 15 Pezda, T.: Polynomial cycles in certain local domains, Acta Arith.LXVI (1994), 11-22. Zbl0803.11063MR1262650
  16. 16 Pezda, T.: Cycles of polynomial mappings in several variables, preprint, 1993. Zbl0804.11059MR1277530
  17. 17 Russo, P. and Walde, R.: Rational periodic points of the quadratic function Qc(x) = x2 + c, Am. Math. Monthly (1994) (to appear). Zbl0804.58036MR1270956
  18. 18 Serre, J.- P.: Local Fields, Springer-Verlag, New York, 1979. Zbl0423.12016MR554237
  19. 19 Serre, J.- P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15 (1972), 259-331. Zbl0235.14012MR387283
  20. 20 Shimura, G.: On the field of definition for a field of automorphic functions.I, Annals of Math.80 (1964), 160-189; II, 81 (1965), 124-165; III, 83 (1965), 377-385. Zbl0222.14027MR167466
  21. 21 Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Forms, Iwanami Shoten and Princeton University Press, Princeton, NJ, 1971. Zbl0221.10029
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  29. 29 Weber, H.: Lehrbuch der Algebra, vol. II, Braunschweig, 1899. JFM30.0093.01

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