Embeddings of maximal tori in orthogonal groups  [ Plongements de tores maximaux dans des groupes orthogonaux ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 1, p. 113-125
Nous donnons des conditions nécessaires et suffisantes pour qu’un groupe orthogonal défini sur un corps global de caractéristique 2 contienne un tore maximal d’un type donné.
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic 2 to contain a maximal torus of a given type.
DOI : https://doi.org/10.5802/aif.2840
Classification:  11E57,  11E12,  20G30
Mots clés: groupes orthogonaux, tores maximaux
@article{AIF_2014__64_1_113_0,
     author = {Bayer-Fluckiger, Eva},
     title = {Embeddings of maximal tori in orthogonal groups},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {1},
     year = {2014},
     pages = {113-125},
     doi = {10.5802/aif.2840},
     mrnumber = {3330542},
     zbl = {06387267},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_1_113_0}
}
Bayer-Fluckiger, Eva. Embeddings of maximal tori in orthogonal groups. Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 113-125. doi : 10.5802/aif.2840. https://www.numdam.org/item/AIF_2014__64_1_113_0/

[1] Brusamarello, Rosali; Chuard-Koulmann, Pascale; Morales, Jorge Orthogonal groups containing a given maximal torus, J. Algebra, Tome 266 (2003) no. 1, pp. 87-101 | Article | MR 1994530 | Zbl 1079.11023

[2] Fiori, Andrew Characterization of special points of orthogonal symmetric spaces, J. Algebra, Tome 372 (2012), pp. 397-419 | Article | MR 2990017 | Zbl pre06180116

[3] Garibaldi, S.; Rapinchuk, A. Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C (Algebra and Number Theory, to appear) | Zbl 1285.20045

[4] Gille, P. Type des tores maximaux des groupes semi-simples, J. Ramanujan Math. Soc., Tome 19 (2004) no. 3, pp. 213-230 | MR 2139505 | Zbl 1193.20057

[5] Lee, T-Y. Embedding functors and their arithmetic properties (Comment. Math. Helv, to appear)

[6] Milne, J. Complex Multiplication (http://www.jmilne.org/math/CourseNotes/cm)

[7] Milnor, John On isometries of inner product spaces, Invent. Math., Tome 8 (1969), pp. 83-97 | Article | MR 249519 | Zbl 0177.05204

[8] O’Meara, O. Timothy Introduction to quadratic forms, Springer-Verlag, Berlin, Classics in Mathematics (2000), pp. xiv+342 (Reprint of the 1973 edition) | MR 1754311 | Zbl 1034.11003

[9] Prasad, Gopal; Rapinchuk, Andrei S. Local-global principles for embedding of fields with involution into simple algebras with involution, Comment. Math. Helv., Tome 85 (2010) no. 3, pp. 583-645 | Article | MR 2653693 | Zbl 1223.11047

[10] Scharlau, Winfried Quadratic and Hermitian forms, Springer-Verlag, Berlin, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Tome 270 (1985), pp. x+421 | MR 770063 | Zbl 0584.10010