Nous donnons des conditions nécessaires et suffisantes pour qu’un groupe orthogonal défini sur un corps global de caractéristique 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 to contain a maximal torus of a given type.
Keywords: Orthogonal groups, maximal tori
Mot clés : groupes orthogonaux, tores maximaux
Bayer-Fluckiger, Eva 1
@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, Tome 64 (2014) no. 1, pp. 113-125. doi : 10.5802/aif.2840. https://aif.centre-mersenne.org/articles/10.5802/aif.2840/
[1] Orthogonal groups containing a given maximal torus, J. Algebra, Volume 266 (2003) no. 1, pp. 87-101 | DOI | MR | Zbl
[2] Characterization of special points of orthogonal symmetric spaces, J. Algebra, Volume 372 (2012), pp. 397-419 | DOI | MR
[3] Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C (Algebra and Number Theory, to appear) | Zbl
[4] Type des tores maximaux des groupes semi-simples, J. Ramanujan Math. Soc., Volume 19 (2004) no. 3, pp. 213-230 | MR | Zbl
[5] Embedding functors and their arithmetic properties (Comment. Math. Helv, to appear)
[6] Complex Multiplication (http://www.jmilne.org/math/CourseNotes/cm)
[7] On isometries of inner product spaces, Invent. Math., Volume 8 (1969), pp. 83-97 | DOI | MR | Zbl
[8] Introduction to quadratic forms, Classics in Mathematics, Springer-Verlag, Berlin, 2000, pp. xiv+342 (Reprint of the 1973 edition) | MR | Zbl
[9] 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] 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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