An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma

Jan-Hendrik Evertse

Acta Arithmetica (1995)

  • Volume: 73, Issue: 3, page 215-248
  • ISSN: 0065-1036

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Jan-Hendrik Evertse. "An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma." Acta Arithmetica 73.3 (1995): 215-248. <http://eudml.org/doc/206819>.

@article{Jan1995,
author = {Jan-Hendrik Evertse},
journal = {Acta Arithmetica},
keywords = {number of solutions of -unit equations; explicit version of the product theorem; Roth's lemma; approximation of algebraic numbers by rationals; quantitative subspace theorem; number of solutions of norm form equations},
language = {eng},
number = {3},
pages = {215-248},
title = {An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma},
url = {http://eudml.org/doc/206819},
volume = {73},
year = {1995},
}

TY - JOUR
AU - Jan-Hendrik Evertse
TI - An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 3
SP - 215
EP - 248
LA - eng
KW - number of solutions of -unit equations; explicit version of the product theorem; Roth's lemma; approximation of algebraic numbers by rationals; quantitative subspace theorem; number of solutions of norm form equations
UR - http://eudml.org/doc/206819
ER -

References

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  2. [2] G. Faltings and G. Wüstholz, Diophantine approximations on projective spaces, Invent. Math. 116 (1994), 109-138. Zbl0805.14011
  3. [3] R. Ferretti, An effective version of Faltings' Product Theorem, Forum Math., to appear. Zbl0860.11038
  4. [4] W. Fulton, Intersection Theory, Band 2, Ergeb. Math. Grenzgeb. (3), Springer, Berlin, 1984. Zbl0541.14005
  5. [5] H. Gillet and C. Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93-174. Zbl0741.14012
  6. [6] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978. Zbl0408.14001
  7. [7] W. Gubler, Höhentheorie, Math. Ann. 298 (1994), 427-456. 
  8. [8] R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977. 
  9. [9] J. de Jong, Ample line bundles and intersection theory, in: Diophantine Approximation and Abelian Varieties, Proc. conf. Soesterberg, Netherlands, 1992, B. Edixhoven and J.-H. Evertse (eds.), Lecture Notes in Math. 1566, Springer, Berlin, 1993, 69-76. Zbl0811.14005
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  12. [12] K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20; Corrigendum, Mathematika 2 (1955), 168. Zbl0064.28501
  13. [13] H. P. Schlickewei, An explicit upper bound for the number of solutions of the S-unit equation, J. Reine Angew. Math. 406 (1990), 109-120. Zbl0693.10016
  14. [14] H. P. Schlickewei, The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273. Zbl0751.11033
  15. [15] W. M. Schmidt, Norm form equations, Ann. of Math. 96 (1972), 526-551. Zbl0226.10024
  16. [16] W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69 (1989), 121-173. Zbl0683.10027
  17. [17] W. M. Schmidt, The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317 (1990), 197-227. Zbl0693.10014
  18. [18] I. R. Shafarevich, Basic Algebraic Geometry, Springer, Berlin, 1977. Zbl0362.14001
  19. [19] C. Soulé, Géométrie d'Arakelov et théorie des nombres transcendants, in: Journées Arithmétiques de Luminy, 1989, G. Lachaud (ed.), Astérisque 198-199-200 (1991), 355-372. 
  20. [20] G. Wüstholz, Multiplicity estimates on group varieties, Ann. of Math. 129 (1989), 471-500. Zbl0675.10024
  21. [21] O. Zariski and P. Samuel, Commutative Algebra, Vol. II, Springer, Berlin, 1960 Zbl0121.27801

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