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
Mot clés : groupes orthogonaux, tores maximaux

Bayer-Fluckiger, Eva 1

1 EPFL-FSB-MATHGEOM-CSAG Station 8 1015 Lausanne (Switzerland) 
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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

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