The Strong abc conjecture over function fields [after McQuillan and Yamanoi]
Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 989, 38 p.
@incollection{AST_2009__326__219_0,
     author = {Gasbarri, Carlo},
     title = {The {Strong} abc conjecture over function fields [after {McQuillan} and {Yamanoi]}},
     booktitle = {S\'eminaire Bourbaki Volume 2007/2008 Expos\'es 982-996},
     series = {Ast\'erisque},
     note = {talk:989},
     pages = {219--256},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {326},
     year = {2009},
     mrnumber = {2605324},
     zbl = {1190.14023},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__326__219_0/}
}
TY  - CHAP
AU  - Gasbarri, Carlo
TI  - The Strong abc conjecture over function fields [after McQuillan and Yamanoi]
BT  - Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
AU  - Collectif
T3  - Astérisque
N1  - talk:989
PY  - 2009
SP  - 219
EP  - 256
IS  - 326
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2009__326__219_0/
LA  - en
ID  - AST_2009__326__219_0
ER  - 
%0 Book Section
%A Gasbarri, Carlo
%T The Strong abc conjecture over function fields [after McQuillan and Yamanoi]
%B Séminaire Bourbaki Volume 2007/2008 Exposés 982-996
%A Collectif
%S Astérisque
%Z talk:989
%D 2009
%P 219-256
%N 326
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2009__326__219_0/
%G en
%F AST_2009__326__219_0
Gasbarri, Carlo. The Strong abc conjecture over function fields [after McQuillan and Yamanoi], dans Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 989, 38 p. http://www.numdam.org/item/AST_2009__326__219_0/

[1] L. V. Ahlfors - "Zur Theorie der Überlagerungsflächen", Acta Math. 65 (1935), p. 157-194. | DOI | JFM | MR

[2] L. V. Ahlfors & L. Sario - Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton Univ. Press., 1960. | MR | Zbl

[3] E. Bombieri & W. Gubler - Heights in Diophantine geometry, New Mathematical Monographs, vol. 4, Cambridge Univ. Press., 2006. | MR | Zbl

[4] M. Brunella - "Courbes entières et feuilletages holomorphes", Enseign. Math. 45 (1999), p. 195-216. | MR | Zbl

[5] X. Chen - "On Vojta 1+ϵ conjecture", preprint arXiv:0705.1727. | Zbl

[6] N. D. Elkies - "ABC implies Mordell", Int. Math. Res. Not. 1991 (1991), p. 99-109. | DOI | MR | Zbl

[7] G. Faltings - "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern", Invent. Math. 73 (1983), p. 349-366. | DOI | EuDML | MR | Zbl

[8] P. Griffiths & J. King - "Nevanlinna theory and holomorphic mappings between algebraic varieties", Acta Math. 130 (1973), p. 145-220. | DOI | MR | Zbl

[9] W. K. Hayman - Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. | MR | Zbl

[10] M. Hindry & J. H. Silverman - "The canonical height and integral points on elliptic curves", Invent Math. 93 (1988), p. 419-450. | DOI | EuDML | MR | Zbl

[11] M. Kim - "Geometric height inequalities and the Kodaira-Spencer map", Composito Math. 105 (1997), p. 43-54. | DOI | MR | Zbl

[12] R. C. Mason - Diophantine equations over function fields, London Math. Soc. Lecture Note Series, vol. 96, Cambridge Univ. Press, 1984. | MR | Zbl

[13] M. Mcquillan - "Diophantine approximations and foliations", Publ. Math. I.H.É.S. 87 (1998), p. 121-174. | DOI | EuDML | MR | Zbl

[14] M. Mcquillan -, "Non commutative Mori theory", preprint I.H.É.S. | Zbl

[15] M. Mcquillan -,"Old and new techniques in function fields arithmetics", preprint.

[16] M. Mcquillan -,"Rational criteria for hyperbolicity", preprint.

[17] Y. Miyaoka - "The orbibundle Miyaoka-Yau-Sakai inequality and an effective Bogomolov-McQuillan theorem", Publ. Res. Inst. Math. Sci. 44 (2008), p. 403-417. | DOI | MR | Zbl

[18] R. Nevanlinna - Analytic functions, Translated from the second German edition by Phillip Emig. Die Grund. Math. Wiss., Band 162, Springer, 1970. | MR | Zbl

[19] A. Nitaj - "The abc conjecture home page", http://www.math.unicaen.fr/nitaj/abc.html. | Zbl

[20] J. Noguchi, J. Winkelmann & K. Yamanoi - "The second main theorem for holomorphic curves into semi-abelian varieties", Acta Math. 188 (2002), p. 129-161. | DOI | MR | Zbl

[21] J. Oesterlé - "Nouvelles approches du "théorème" de Fermat", Séminaire Bourbaki, Vol. 1987/88, exposé n° 694, Astérisque 161-162 (1988), p. 165-186. | EuDML | Numdam | MR | Zbl

[22] C. F. Osgood - "Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better", J. Number Theory 21 (1985), p. 347-389. | DOI | MR | Zbl

[23] A. Sauer - "Deficient rational functions and Ahlfors's theory of covering surfaces", Ark. Mat. 39 (2001), p. 151-155. | DOI | MR | Zbl

[24] J-P. Serre - Lectures on the Mordell-Weil theorem, Aspects of Mathematics, E15, Friedr. Vieweg & Sohn, 1989. | MR | Zbl

[25] L. Szpiro - "Discriminant et conducteur des courbes elliptiques", Astérisque 183 (1990), p. 7-18. | Numdam | MR | Zbl

[26] P. Vojta - Diophantine approximations and value distribution theory, Lecture Notes in Math., vol. 1239, Springer, 1987. | MR | Zbl

[27] P. Vojta -, "On algebraic points on curves", Compositio Math. 78 (1991), p. 29-36. | EuDML | Numdam | MR | Zbl

[28] A. Wiles - "Modular elliptic curves and Fermat's last theorem", Ann. of Math. 141 (1995), p. 443-551. | DOI | MR | Zbl

[29] K. Yamanoi - "The second main theorem for small functions and related problems", Acta Math. 192 (2004), p. 225-294. | DOI | MR | Zbl

[30] K. Yamanoi -, "Defect relation for rational functions as targets", Forum Math. 17 (2005), p. 169-189. | DOI | MR | Zbl

[31] K. Yamanoi -, "On the truncated small function theorem in Nevanlinna theory", Internat. J. Math. 17 (2006), p. 417-440. | DOI | MR | Zbl