Diophantine approximation and deformation

Minhyoung Kim; Dinesh S. Thakur; José Felipe Voloch

Bulletin de la Société Mathématique de France (2000)

  • Volume: 128, Issue: 4, page 585-598
  • ISSN: 0037-9484

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Kim, Minhyoung, Thakur, Dinesh S., and Voloch, José Felipe. "Diophantine approximation and deformation." Bulletin de la Société Mathématique de France 128.4 (2000): 585-598. <http://eudml.org/doc/87841>.

@article{Kim2000,
author = {Kim, Minhyoung, Thakur, Dinesh S., Voloch, José Felipe},
journal = {Bulletin de la Société Mathématique de France},
keywords = {deformation; positive characteristic; Kodaira-Spencer map; Riccati condition; height inequalities for algebraic points},
language = {eng},
number = {4},
pages = {585-598},
publisher = {Société mathématique de France},
title = {Diophantine approximation and deformation},
url = {http://eudml.org/doc/87841},
volume = {128},
year = {2000},
}

TY - JOUR
AU - Kim, Minhyoung
AU - Thakur, Dinesh S.
AU - Voloch, José Felipe
TI - Diophantine approximation and deformation
JO - Bulletin de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 128
IS - 4
SP - 585
EP - 598
LA - eng
KW - deformation; positive characteristic; Kodaira-Spencer map; Riccati condition; height inequalities for algebraic points
UR - http://eudml.org/doc/87841
ER -

References

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  1. [BS] BAUM (L.), SWEET (M.). — Continued fractions of algebraic power series in characteristic 2, Ann. of Math., t. 103, 1976, p. 593-610. Zbl0312.10024MR53 #13127
  2. [K] KIM (M.). — Geometric height inequalities and the Kodaira-Spencer map, Compositio Math., t. 105, 1997, p. 43-54. Zbl0871.14020MR98j:14029
  3. [LdM1] LASJAUNIAS (A.), DE MATHAN (B.). — Thue's theorem in positive characteristic, J. reine angew. Math., t. 473, 1996, p. 195-206. Zbl0844.11046MR97c:11076
  4. [LdM2] LASJAUNIAS (A.), DE MATHAN (B.). — Differential equations and Diophantine approximation in positive characteristic, Monatshefte Math., t. 128, 1999, p. 1-6. Zbl0953.11024MR2000f:11091
  5. [M] MAHLER (K.). — On a theorem of Liouville in fields of positive characteristic, Can. J. Math., t. 1, 1949, p. 397-400. Zbl0033.35203MR11,159e
  6. [O1] OSGOOD (C.). — An effective lower bound on the diophantine approximation of algebraic functions by rational functions, Mathematika, t. 20, 1973, p. 4-15. Zbl0269.10017MR50 #7050
  7. [O2] OSGOOD (C.). — Effective bounds on the diophantine approximation of algebraic functions over fields of arbitrary characteristic and applications to differential equations, Indag. Math., t. 37, 1975, p. 104-119. Zbl0302.10034MR52 #8048a
  8. [Sc1] SCHMIDT (W.). — On Osgood's effective Thue theorem for algebraic functions, Comm. Pure Applied Math., t. 29, 1976, p. 759-773. Zbl0333.10019MR54 #7393
  9. [Sc2] SCHMIDT (W.). — On continued fractions and diophantine approximation in power series fields, to appear in Acta Arithmetica. Zbl0987.11041
  10. [Sc3] SCHMIDT (W.). — Diophantine approximation, Lecture Notes in Math., t. 785, Springer, Berlin, 1980. Zbl0421.10019MR81j:10038
  11. [T] THAKUR (D.). — Diophantine approximation exponents and continued fractions for algebraic power series, J. Number Theory, t. 79, 1999, p. 284-291. Zbl0966.11029MR2000j:11104
  12. [V1] VOLOCH (J.F.). — Diophantine approximation in positive characteristic, Periodica Math. Hungarica, t. 19, 1988, p. 217-225. Zbl0661.10050MR89h:11045
  13. [V2] VOLOCH (J.F.). — Diophantine approximation in characteristic p, Monatsh. Math., t. 119, 1995, p. 321-325. Zbl0827.11039MR96b:11099
  14. [V3] VOLOCH (J.F.). — Diophantine geometry in characteristic p : a survey, in Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica, Cambridge Univ. Press, t. XXXVII, 1997, p. 260-278. Zbl0905.14011MR99c:11081
  15. [Voj1] VOJTA (P.). — Diophantine approximations and value distribution theory, Lecture Notes in Math., Springer, Berlin, t. 1239, 1987. Zbl0609.14011MR91k:11049
  16. [Voj2] VOJTA (P.). — On algebraic points on curves, Comp. Math., t. 78, 1991, p. 29-36. Zbl0731.14015MR93b:11080

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