ArticleOriginal scientific text
Title
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
Authors 1
Affiliations
- Department of Mathematics and Computer Science, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Bibliography
- G. Faltings, Diophantine approximation on abelian varieties, Ann. of Math. 133 (1991), 549-576.
- G. Faltings and G. Wüstholz, Diophantine approximations on projective spaces, Invent. Math. 116 (1994), 109-138.
- R. Ferretti, An effective version of Faltings' Product Theorem, Forum Math., to appear.
- W. Fulton, Intersection Theory, Band 2, Ergeb. Math. Grenzgeb. (3), Springer, Berlin, 1984.
- H. Gillet and C. Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93-174.
- P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978.
- W. Gubler, Höhentheorie, Math. Ann. 298 (1994), 427-456.
- R. Hartshorne, Algebraic Geometry, Springer, Berlin, 1977.
- 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.
- P. Philippon, Sur des hauteurs alternatives, I, Math. Ann. 289 (1991), 255-283.
- M. van der Put, The Product theorem, 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, 77-82.
- K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 1-20; Corrigendum, Mathematika 2 (1955), 168.
- 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.
- H. P. Schlickewei, The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273.
- W. M. Schmidt, Norm form equations, Ann. of Math. 96 (1972), 526-551.
- W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69 (1989), 121-173.
- W. M. Schmidt, The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317 (1990), 197-227.
- I. R. Shafarevich, Basic Algebraic Geometry, Springer, Berlin, 1977.
- 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.
- G. Wüstholz, Multiplicity estimates on group varieties, Ann. of Math. 129 (1989), 471-500.
- O. Zariski and P. Samuel, Commutative Algebra, Vol. II, Springer, Berlin, 1960