We give a classification, up to consideration of component groups, of sub-Shimura varieties of those Shimura Varieties attached to orthogonal groups of signature over .
Nous donnons une classification, sans tenir compte des groupes de composantes, des sous-variétés de Shimura des variétés de Shimura attachées aux groupes orthogonaux de signature sur .
Révisé le :
Accepté le :
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DOI : 10.5802/jtnb.1060
Keywords: Shimura Varieties, Cycles
Fiori, Andrew 1
CC-BY-ND 4.0
@article{JTNB_2018__30_3_979_0,
author = {Fiori, Andrew},
title = {Sub-Shimura {Varieties} for type $O(2,n)$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {979--990},
year = {2018},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {30},
number = {3},
doi = {10.5802/jtnb.1060},
mrnumber = {3938637},
zbl = {1420.14049},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.1060/}
}
TY - JOUR AU - Fiori, Andrew TI - Sub-Shimura Varieties for type $O(2,n)$ JO - Journal de théorie des nombres de Bordeaux PY - 2018 SP - 979 EP - 990 VL - 30 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://www.numdam.org/articles/10.5802/jtnb.1060/ DO - 10.5802/jtnb.1060 LA - en ID - JTNB_2018__30_3_979_0 ER -
Fiori, Andrew. Sub-Shimura Varieties for type $O(2,n)$. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 979-990. doi: 10.5802/jtnb.1060
[1] Tate twists of Hodge structures arising from abelian varieties of type IV, J. Pure Appl. Algebra, Volume 216 (2012) no. 5, pp. 1164-1170 | Zbl | MR | DOI
[2] Automorphic forms on and infinite products, Invent. Math., Volume 120 (1995) no. 1, pp. 161-213 | Zbl | MR | DOI
[3] Borcherds products on O(2,) and Chern classes of Heegner divisors, Lecture Notes in Mathematics, 1780, Springer, 2002 | Zbl | MR
[4] Special values of Green functions at big CM points, Int. Math. Res. Not., Volume 2012 (2012) no. 9, pp. 1917-1967 | Zbl | MR
[5] CM-values of Hilbert modular functions, Invent. Math., Volume 163 (2006) no. 2, pp. 229-288 | Zbl | MR | DOI
[6] Characterization of special points of orthogonal symmetric spaces, J. Algebra, Volume 372 (2012), pp. 397-419 | MR | DOI
[7] Questions in the Theory of Orthogonal Shimura Varieties, McGill University (Canada) (2013) (Ph. D. Thesis)
[8] Transfer and local density for hermitian lattices, Ann. Math. Qué., Volume 42 (2018) no. 1, pp. 49-78 | Zbl | MR | DOI
[9] Representation theory. A first course, Readings in Mathematics, Graduate Texts in Mathematics, 129, Springer, 1991 | Zbl
[10] On a conjecture of Bruinier-Yang, Oberwolfach Report, Volume 32 (2012), pp. 21-24
[11] Heegner points and derivatives of -series, Invent. Math., Volume 84 (1986) no. 2, pp. 225-320 | Zbl | MR | DOI
[12] Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics, 34, American Mathematical Society, 1978 (Corrected reprint of the 1978 original) | Zbl
[13] Algebraic cycles on Shimura varieties of orthogonal type, Duke Math. J., Volume 86 (1997) no. 1, pp. 39-78 | MR
[14] Arithmetic Hirzebruch-Zagier cycles, J. Reine Angew. Math., Volume 515 (1999), pp. 155-244 | Zbl | MR | DOI
[15] Introduction to Shimura varieties, Harmonic analysis, the trace formula, and Shimura varieties (Clay Mathematics Proceedings), Volume 4, American Mathematical Society, 2005, pp. 265-378 | MR | Zbl
[16] Holomorphic imbeddings of symmetric domains into a Siegel space, Am. J. Math., Volume 87 (1965), pp. 425-461 | Zbl | MR | DOI
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