no. 1
Embeddings of maximal tori in orthogonal groups
Bayer-Fluckiger, Eva1
1 EPFL-FSB-MATHGEOM-CSAG Station 8 1015 Lausanne (Switzerland)
Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 113-125.

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.

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.

DOI: 10.5802/aif.2840
Classification: 11E57, 11E12, 20G30
Keywords: Orthogonal groups, maximal tori
Bayer-Fluckiger, Eva 1

1 EPFL-FSB-MATHGEOM-CSAG Station 8 1015 Lausanne (Switzerland) 
@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},
     pages = {113--125},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {64},
     number = {1},
     year = {2014},
     doi = {10.5802/aif.2840},
     mrnumber = {3330542},
     zbl = {06387267},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2840/}
}
TY  - JOUR
AU  - Bayer-Fluckiger, Eva
TI  - Embeddings of maximal tori in orthogonal groups
JO  - Annales de l'Institut Fourier
PY  - 2014
SP  - 113
EP  - 125
VL  - 64
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2840/
DO  - 10.5802/aif.2840
LA  - en
ID  - AIF_2014__64_1_113_0
ER  - 
%0 Journal Article
%A Bayer-Fluckiger, Eva
%T Embeddings of maximal tori in orthogonal groups
%J Annales de l'Institut Fourier
%D 2014
%P 113-125
%V 64
%N 1
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2840/
%R 10.5802/aif.2840
%G en
%F AIF_2014__64_1_113_0
Bayer-Fluckiger, Eva. Embeddings of maximal tori in orthogonal groups. Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 113-125. doi : 10.5802/aif.2840. https://aif.centre-mersenne.org/articles/10.5802/aif.2840/

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

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

[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

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

[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., Volume 8 (1969), pp. 83-97 | DOI | MR | Zbl

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

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

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

Cited by Sources: