@article{PMIHES_2016__123__333_0, author = {Klingler, B. and Ullmo, E. and Yafaev, A.}, title = {The hyperbolic {Ax-Lindemann-Weierstra{\ss}} conjecture}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {333--360}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {123}, year = {2016}, doi = {10.1007/s10240-015-0078-9}, zbl = {1372.14016}, mrnumber = {3502100}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-015-0078-9/} }
TY - JOUR AU - Klingler, B. AU - Ullmo, E. AU - Yafaev, A. TI - The hyperbolic Ax-Lindemann-Weierstraß conjecture JO - Publications Mathématiques de l'IHÉS PY - 2016 SP - 333 EP - 360 VL - 123 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-015-0078-9/ DO - 10.1007/s10240-015-0078-9 LA - en ID - PMIHES_2016__123__333_0 ER -
%0 Journal Article %A Klingler, B. %A Ullmo, E. %A Yafaev, A. %T The hyperbolic Ax-Lindemann-Weierstraß conjecture %J Publications Mathématiques de l'IHÉS %D 2016 %P 333-360 %V 123 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-015-0078-9/ %R 10.1007/s10240-015-0078-9 %G en %F PMIHES_2016__123__333_0
Klingler, B.; Ullmo, E.; Yafaev, A. The hyperbolic Ax-Lindemann-Weierstraß conjecture. Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 333-360. doi : 10.1007/s10240-015-0078-9. http://www.numdam.org/articles/10.1007/s10240-015-0078-9/
[1.] Smooth Compactification of Locally Symmetric Varieties (1975) | Zbl
[2.] On Schanuel’s conjecture, Ann. Math., Volume 93 (1971), pp. 1-24 | DOI | MR | Zbl
[3.] Compactification of arithmetic quotients of bounded symmetric domains, Ann. Math., Volume 84 (1966), pp. 442-528 | DOI | MR | Zbl
[4.] Introduction aux Groupes Arithmétiques (1969) | Zbl
[5.] C. Daw and M. Orr, Heights of pre-special points of Shimura varieties, Math. Ann., to appear, | arXiv
[6.] Variétés de Shimura: interprétation modulaire et techniques de construction de modèles canoniques, Automorphic Forms, Representations, and -Functions, Part. 2 (1979), pp. 247-290 | DOI | Zbl
[7.] Tame Topology and o-Minimal Structures (1998) | DOI | MR | Zbl
[8.] On the real exponential field with restricted analytic functions, Isr. J. Math., Volume 85 (1994), pp. 19-56 | DOI | MR | Zbl
[9.] Subvarieties of Shimura varieties, Ann. Math., Volume 157 (2003), pp. 621-645 | DOI | MR | Zbl
[10.] Sur l’algébricité des ensembles analytiques complexes, J. Reine Angew. Math., Volume 329 (1981), pp. 215-220 | MR | Zbl
[11.] Volumes of complex analytic subvarieties of Hermitian symmetric spaces, Am. J. Math., Volume 124 (2002), pp. 1221-1246 | DOI | MR | Zbl
[12.] The André-Oort conjecture, Ann. Math., Volume 180 (2014), pp. 867-925 | DOI | MR | Zbl
[13.] Über die Zahl , Math. Ann., Volume 20 (1882), pp. 213-225 | DOI | JFM | MR
[14.] Discrete Subgroups of Semisimple Lie Groups (1991) | DOI | MR | Zbl
[15.] Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds (1989) | DOI | MR | Zbl
[16.] On the Zariski closure of a germ of totally geodesic complex submanifold on a subvariety of a complex hyperbolic space form of finite volume, Complex Analysis (2010) | DOI | MR | Zbl
[17.] Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric, J. Eur. Math. Soc., Volume 14 (2012), pp. 1617-1656 | DOI | MR | Zbl
[18.] Linearity properties of Shimura varieties. I, J. Algeb. Geom., Volume 7 (1998), pp. 539-567 | MR | Zbl
[19.] Hirzebruch’s proportionality theorem in the non-cocompact case, Invent. Math., Volume 42 (1979), pp. 239-272 | DOI | MR | Zbl
[20.] Definability of restricted theta functions and families of Abelian varieties, Duke Math. J., Volume 162 (2013), pp. 731-765 | DOI | MR | Zbl
[21.] Tame complex analysis and o-minimality, Proceedings of the ICM (2010) (Available on first author’s web-page) | MR | Zbl
[22.] Automorphic Functions and the Geometry of Classical Domains (1969) (translated from the Russian) | MR | Zbl
[23.] O-minimality and the Andre-Oort conjecture for , Ann. Math., Volume 173 (2011), pp. 1779-1840 | DOI | MR | Zbl
[24.] The rational points on a definable set, Duke Math. J., Volume 133 (2006), pp. 591-616 | DOI | MR | Zbl
[25.] The André-Oort conjecture for the moduli space of abelian surfaces, Compos. Math., Volume 149 (2013), pp. 204-216 | DOI | MR | Zbl
[26.] Ax-Lindemann for , Ann. Math., Volume 179 (2014), pp. 659-681 | DOI | MR | Zbl
[27.] Rational points in periodic analytic sets and the Manin-Mumford conjecture, Atti Accad. Naz. Lincei, Rend. Lincei, Mat. Appl., Volume 19 (2008), pp. 149-162 | DOI | MR | Zbl
[28.] Algebraic Structures of Symmetric Domains (1980) | MR | Zbl
[29.] T. Scanlon, O-minimality as an approach to the André-Oort conjecture, preprint (2012). Available on author’s web-page. | MR
[30.] Applications du théorème d’Ax-Lindemann hyperbolique, Compos. Math., Volume 150 (2014), pp. 175-190 | DOI | MR | Zbl
[31.] Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture, Ann. Math., Volume 180 (2014), pp. 823-865 | DOI | MR | Zbl
[32.] A characterisation of special subvarieties, Mathematika, Volume 57 (2011), pp. 263-273 | DOI | MR | Zbl
[33.] Nombre de classes des tores de multiplication complexe et bornes inférieures pour orbites Galoisiennes de points spéciaux, Bull. Soc. Math. Fr., Volume 143 (2015), pp. 197-228 | DOI | MR | Zbl
[34.] Hyperbolic Ax-Lindemann theorem in the cocompact case, Duke Math. J., Volume 163 (2014), pp. 433-463 | DOI | MR | Zbl
[35.] Brauer-Siegel theorem for tori and lower bounds for Galois orbits of special points, J. Am. Math. Soc., Volume 25 (2012), pp. 1091-1117 | DOI | MR | Zbl
[36.] K. Weierstraß, Zu Lindemanns Abhandlung: “Über die Ludolph’sche Zahl”, Berl. Ber. (1885), 1067–1086. | JFM
[37.] Generalized Cailey transformations of bounded symmetric domains, Am. J. Math., Volume 87 (1965), pp. 899-939 | DOI | MR | Zbl
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