On détermine les groupes algébriques qui ont une étroite relation avec les inégalités de Roth.
We determine the algebraic groups which have a close relation to the Roth inequalities.
@article{JTNB_2012__24_2_257_0, author = {Fujimori, Masami}, title = {The algebraic groups leading to the {Roth} inequalities}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {257--292}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {24}, number = {2}, year = {2012}, doi = {10.5802/jtnb.796}, zbl = {1276.11120}, mrnumber = {2950692}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.796/} }
TY - JOUR AU - Fujimori, Masami TI - The algebraic groups leading to the Roth inequalities JO - Journal de théorie des nombres de Bordeaux PY - 2012 SP - 257 EP - 292 VL - 24 IS - 2 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.796/ DO - 10.5802/jtnb.796 LA - en ID - JTNB_2012__24_2_257_0 ER -
%0 Journal Article %A Fujimori, Masami %T The algebraic groups leading to the Roth inequalities %J Journal de théorie des nombres de Bordeaux %D 2012 %P 257-292 %V 24 %N 2 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.796/ %R 10.5802/jtnb.796 %G en %F JTNB_2012__24_2_257_0
Fujimori, Masami. The algebraic groups leading to the Roth inequalities. Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 257-292. doi : 10.5802/jtnb.796. http://www.numdam.org/articles/10.5802/jtnb.796/
[1] Y. André, Slope filtrations. Confluentes Math. 1 (2009), 1–85 (arXiv:0812.3921v2). | MR
[2] A. Borel, Linear Algebraic Groups, Second Enlarged Edition. Graduate Texts in Math. 126, Springer-Verlag, New York, 1991. | MR | Zbl
[3] J.-F. Dat, S. Orlik, and M. Rapoport, Period Domains over Finite and -adic Fields. Cambridge Tracts in Math. 183, Cambridge Univ. Press, New York, 2010. | MR
[4] P. Deligne and J. S. Milne, Tannakian Categories. In Hodge Cycles, Motives, and Shimura Varieties, Lect. Notes in Math. 900, 101–228, Springer-Verlag, Berlin Heidelberg, 1982. | MR | Zbl
[5] J.-H. Evertse, The subspace theorem and twisted heights. Preprint, 32pp. (http://www.math.leidenuniv.nl/~evertse/publications.shtml)
[6] G. Faltings, Mumford-Stabilität in der algebraischen Geometrie. Proceedings of the International Congress of Mathematicians 1994, Zürich, Switzerland, 648–655, Birkhäuser Verlag, Basel, Switzerland, 1995. | MR | Zbl
[7] G. Faltings and G. Wüstholz, Diophantine approximations on projective spaces. Invent. Math. 116 (1994), 109–138. | MR | Zbl
[8] M. Fujimori, On systems of linear inequalities. Bull. Soc. Math. France 131 (2003), 41–57. Corrigenda. ibid. 132 (2004), 613–616. | Numdam | MR
[9] M. Rapoport, Analogien zwischen den Modulräumen von Vektorbündeln und von Flaggen. Jahresber. Deutsch. Math.-Verein. 99 (1997), 164–180. | MR | Zbl
[10] M. Rapoport, Period domains over finite and local fields. In Algebraic Geometry—Santa Cruz 1995, Proc. Sympos. Pure Math. 62, 361–381, Amer. Math. Soc., Providence, RI, 1997. | MR | Zbl
[11] N. S. Rivano, Catégories Tannakiennes. Lect. Notes in Math. 265, Springer-Verlag, Berlin Heidelberg, 1972. | MR | Zbl
[12] W. M. Schmidt, Diophantine Approximation. Lect. Notes in Math. 785, Springer-Verlag, Berlin Heidelberg, 1980. | MR | Zbl
[13] B. Totaro, Tensor products in -adic Hodge theory. Duke Math. J. 83 (1996), 79–104. | MR | Zbl
Cité par Sources :