Sub-Shimura Varieties for type O(2,n)
Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 979-990.

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 (2,n) sur .

We give a classification, up to consideration of component groups, of sub-Shimura varieties of those Shimura Varieties attached to orthogonal groups of signature (2,n) over .

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1060
Classification : 14G35
Mots clés : Shimura Varieties, Cycles
Andrew Fiori 1

1 Mathematics and Computer Science, C526 University Hall, 4401 University Drive, University of Lethbridge, Lethbridge, Alberta, T1K 3M4
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{JTNB_2018__30_3_979_0,
     author = {Andrew Fiori},
     title = {Sub-Shimura {Varieties} for type $O(2,n)$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {979--990},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {30},
     number = {3},
     year = {2018},
     doi = {10.5802/jtnb.1060},
     zbl = {1420.14049},
     mrnumber = {3938637},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1060/}
}
TY  - JOUR
AU  - Andrew Fiori
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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1060/
DO  - 10.5802/jtnb.1060
LA  - en
ID  - JTNB_2018__30_3_979_0
ER  - 
%0 Journal Article
%A Andrew Fiori
%T Sub-Shimura Varieties for type $O(2,n)$
%J Journal de théorie des nombres de Bordeaux
%D 2018
%P 979-990
%V 30
%N 3
%I Société Arithmétique de Bordeaux
%U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1060/
%R 10.5802/jtnb.1060
%G en
%F JTNB_2018__30_3_979_0
Andrew Fiori. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1060/

[1] Salman Abdulali Tate twists of Hodge structures arising from abelian varieties of type IV, J. Pure Appl. Algebra, Volume 216 (2012) no. 5, pp. 1164-1170 | DOI | MR | Zbl

[2] Richard E. Borcherds Automorphic forms on O s+2,2 (R) and infinite products, Invent. Math., Volume 120 (1995) no. 1, pp. 161-213 | DOI | MR | Zbl

[3] Jan H. Bruinier Borcherds products on O(2,l) and Chern classes of Heegner divisors, Lecture Notes in Mathematics, 1780, Springer, 2002 | MR | Zbl

[4] Jan H. Bruinier; Stephen S. Kudla; Tonghai Yang Special values of Green functions at big CM points, Int. Math. Res. Not., Volume 2012 (2012) no. 9, pp. 1917-1967 | MR | Zbl

[5] Jan Hendrik Bruinier; Tonghai Yang CM-values of Hilbert modular functions, Invent. Math., Volume 163 (2006) no. 2, pp. 229-288 | DOI | MR | Zbl

[6] Andrew Fiori Characterization of special points of orthogonal symmetric spaces, J. Algebra, Volume 372 (2012), pp. 397-419 | DOI | MR

[7] Andrew Fiori Questions in the Theory of Orthogonal Shimura Varieties, McGill University (Canada) (2013) (Ph. D. Thesis)

[8] Andrew Fiori Transfer and local density for hermitian lattices, Ann. Math. Qué., Volume 42 (2018) no. 1, pp. 49-78 | DOI | MR | Zbl

[9] William Fulton; Joe Harris Representation theory. A first course, Readings in Mathematics, Graduate Texts in Mathematics, 129, Springer, 1991 | Zbl

[10] Eyal Z. Goren On a conjecture of Bruinier-Yang, Oberwolfach Report, Volume 32 (2012), pp. 21-24

[11] Benedict H. Gross; Don B. Zagier Heegner points and derivatives of L-series, Invent. Math., Volume 84 (1986) no. 2, pp. 225-320 | DOI | MR | Zbl

[12] Sigurdur Helgason Differential geometry, Lie groups, and symmetric spaces, Graduate Studies in Mathematics, 34, American Mathematical Society, 1978 (Corrected reprint of the 1978 original) | Zbl

[13] Stephen S. Kudla Algebraic cycles on Shimura varieties of orthogonal type, Duke Math. J., Volume 86 (1997) no. 1, pp. 39-78 | MR

[14] Stephen S. Kudla; Michael Rapoport Arithmetic Hirzebruch-Zagier cycles, J. Reine Angew. Math., Volume 515 (1999), pp. 155-244 | DOI | MR | Zbl

[15] James S. Milne 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] Ichirô Satake Holomorphic imbeddings of symmetric domains into a Siegel space, Am. J. Math., Volume 87 (1965), pp. 425-461 | DOI | MR | Zbl

Cité par Sources :