@article{CML_2010__2_3_351_0,
author = {Chambert-Loir, Antoine and Tschinkel, Yuri},
title = {Igusa integrals and volume asymptotics in analytic and adelic geometry},
journal = {Confluentes Mathematici},
pages = {351--429},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {3},
year = {2010},
doi = {10.1142/S1793744210000223},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744210000223/}
}
TY - JOUR AU - Chambert-Loir, Antoine AU - Tschinkel, Yuri TI - Igusa integrals and volume asymptotics in analytic and adelic geometry JO - Confluentes Mathematici PY - 2010 SP - 351 EP - 429 VL - 2 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744210000223/ DO - 10.1142/S1793744210000223 LA - en ID - CML_2010__2_3_351_0 ER -
%0 Journal Article %A Chambert-Loir, Antoine %A Tschinkel, Yuri %T Igusa integrals and volume asymptotics in analytic and adelic geometry %J Confluentes Mathematici %D 2010 %P 351-429 %V 2 %N 3 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744210000223/ %R 10.1142/S1793744210000223 %G en %F CML_2010__2_3_351_0
Chambert-Loir, Antoine; Tschinkel, Yuri. Igusa integrals and volume asymptotics in analytic and adelic geometry. Confluentes Mathematici, Tome 2 (2010) no. 3, pp. 351-429. doi : 10.1142/S1793744210000223. http://www.numdam.org/articles/10.1142/S1793744210000223/
[1] A. Baker , Transcendental Number Theory ( Cambridge Univ. Press , 1975 ) .
[2] V. V. Batyrev, New Trends in Algebraic Geometry (Cambridge Univ. Press, Warwick, 1996) pp. 1–11.
[3] V. V. Batyrev and Yu. I. Manin, Math. Ann. 286, 27 (1990), DOI: 10.1007/BF01453564.
[4] V. V. Batyrev and Yu. Tschinkel, Internat. Math. Res. Notices 12, 591 (1995).
[5] V. V. Batyrev and Yu. Tschinkel, J. Math. Sci. 82, 3220 (1996), DOI: 10.1007/BF02362469.
[6] B. J. Birch, Proc. London Math. Soc. A 265, 245 (1962), DOI: 10.1098/rspa.1962.0007.
[7] M. Borovoi and Z. Rudnick, Invent. Math. 119, 37 (1995), DOI: 10.1007/BF01245174.
[8] R. Brauer, Ann. Math. 48, 502 (1947), DOI: 10.2307/1969183.
[9] R. de la Bretèche, J. Number Th. 87, 315 (2001).
[10] M. Brion and S. Kumar , Frobenius Splitting Methods in Geometry and Representation Theory , Progress in Mathematics 231 ( Birkhäuser , 2005 ) .
[11] F. Bruhat and J. Tits, Publ. Math. Inst. Hautes Études Sci. 5 (1972).
[12] A. Chambert-Loir and Yu. Tschinkel, J. Number Th. 85, 172 (2000), DOI: 10.1006/jnth.2000.2539.
[13] A. Chambert-Loir and Yu. Tschinkel, Invent. Math. 148, 421 (2002), DOI: 10.1007/s002220100200.
[14] A. Chambert-Loir and Yu. Tschinkel, Integral points of bounded height on partial equivariant compactifications of vector groups , arXiv:0912.4751 .
[15] A. Chambert-Loir and Yu. Tschinkel, Integral points of bounded height on toric varieties , arXiv:1006.3345 .
[16] H. Clemens, Trans. Amer. Math. Soc. 136, 93 (1969), DOI: 10.1090/S0002-9947-1969-0233814-9.
[17] R. Cluckers, G. Comte and F. Loeser, Local metric properties and regular stratifications of p-adic definable sets , arXiv:0910.0799 .
[18] J.-L. Colliot-Thélène and J.-J. Sansuc, Duke Math. J. 54, 375 (1987), DOI: 10.1215/S0012-7094-87-05420-2.
[19] C. De Concini and C. Procesi, Invariant Theory, Lecture Notes in Math 996 (Springer, Montecatini, 1982) pp. 1–44.
[20] P. Deligne, Publ. Math. Inst. Hautes Études Sci. 43, 273 (1974), DOI: 10.1007/BF02684373.
[21] J. Denef, Amer. J. Math. 109, 991 (1987), DOI: 10.2307/2374583.
[22] W. Duke, Z. Rudnick and P. Sarnak, Duke Math. J. 71, 143 (1993), DOI: 10.1215/S0012-7094-93-07107-4.
[23] A. Eskin and C. McMullen, Duke Math. J. 71, 181 (1993), DOI: 10.1215/S0012-7094-93-07108-6.
[24] A. Eskin, S. Mozes and N. Shah, Ann. Math. 143, 253 (1996), DOI: 10.2307/2118644.
[25] J. Franke, Yu. I. Manin and Yu. Tschinkel, Invent. Math. 95, 421 (1989), DOI: 10.1007/BF01393904.
[26] G. L. Gordon, Trans. Amer. Math. Soc. 261, 93 (1980), DOI: 10.1090/S0002-9947-1980-0576865-1.
[27] A. Gorodnik, F. Maucourant and H. Oh, Ann. Sci. École Norm. Sup. 41, 385 (2008).
[28] A. Gorodnik, H. Oh and N. Shah, Amer. J. Math. 131, 1 (2009).
[29] B. Hassett and Yu. Tschinkel, Duke Math. J. 120, 577 (2003).
[30] M. Hindry and J. H. Silverman , Diophantine Geometry. An Introduction , Graduate Texts in Mathematics 201 ( Springer , 2000 ) .
[31] J.-I. Igusa, J. Reine Angew. Math 269 (1974) pp. 110–130.
[32] J.-I. Igusa, J. Reine Angew. Math. 279, 307 (1975).
[33] F. Knop, The Luna-Vust theory of spherical embeddings, Proc. of the Hyderabad Conference on Algebraic Groups (Manoj Prakashan, 1989) pp. 225–249.
[34] S. Lang , Fundamentals of Diophantine Geometry ( Springer , 1983 ) .
[35] S. Lang and A. Weil, Amer. J. Math. 76, 819 (1954), DOI: 10.2307/2372655.
[36] F. Maucourant, Duke Math. J. 136, 357 (2007), DOI: 10.1215/S0012-7094-07-13626-3.
[37] J. S. Milne , Étale Cohomology , Math. Notes ( Princeton Univ. Press , 1980 ) .
[38] E. Peyre, Duke Math. J. 79, 101 (1995), DOI: 10.1215/S0012-7094-95-07904-6.
[39] E. Peyre (ed.) , Nombre et Répartition des Points de Hauteur Bornée ( Astérisque , 1998 ) .
[40] E. Peyre, Nombre et Répartition des Points de Hauteur Bornée, ed. () pp. 259–298.
[41] P. Salberger, Nombre et Répartition des Points de Hauteur Bornée () pp. 91–258.
[42] J.-P. Serre, Inst. Hautes Études Sci. Publ. Math. 323 (1981).
[43] J.-P. Serre , Lectures on the Mordell–Weil Theorem , 3rd edn. , Aspects of Mathematics , ed. ( Friedr. Vieweg & Sohn , 1997 ) .
[44] N. A. Shah, Sankhyā Ser. A 62, 386 (2000).
[45] J. Shalika, R. Takloo-Bighash and Yu. Tschinkel, J. Amer. Math. Soc. 20, 1135 (2007), DOI: 10.1090/S0894-0347-07-00572-3.
[46] A. Skorobogatov , Torsors and Rational Points , Cambridge Tracts in Mathematics 144 ( Cambridge Univ. Press , 2001 ) .
[47] A. Weil , Adeles and Algebraic Groups , Progr. Math. ( Birkhäuser , 1982 ) .
[48] A. Weil , Basic Number Theory ( Springer , 1995 ) .
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