Embeddings of maximal tori in orthogonal groups

Eva Bayer-Fluckiger[1]

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

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 113-125
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Bayer-Fluckiger, Eva. "Embeddings of maximal tori in orthogonal groups." Annales de l’institut Fourier 64.1 (2014): 113-125. <http://eudml.org/doc/275454>.

@article{Bayer2014,
abstract = {We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic $\ne 2$ to contain a maximal torus of a given type.},
affiliation = {EPFL-FSB-MATHGEOM-CSAG Station 8 1015 Lausanne (Switzerland)},
author = {Bayer-Fluckiger, Eva},
journal = {Annales de l’institut Fourier},
keywords = {Orthogonal groups; maximal tori; orthogonal groups; maximal torus; étale algebra},
language = {eng},
number = {1},
pages = {113-125},
publisher = {Association des Annales de l’institut Fourier},
title = {Embeddings of maximal tori in orthogonal groups},
url = {http://eudml.org/doc/275454},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Bayer-Fluckiger, Eva
TI - Embeddings of maximal tori in orthogonal groups
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 113
EP - 125
AB - We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic $\ne 2$ to contain a maximal torus of a given type.
LA - eng
KW - Orthogonal groups; maximal tori; orthogonal groups; maximal torus; étale algebra
UR - http://eudml.org/doc/275454
ER -

References

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  1. Rosali Brusamarello, Pascale Chuard-Koulmann, Jorge Morales, Orthogonal groups containing a given maximal torus, J. Algebra 266 (2003), 87-101 Zbl1079.11023MR1994530
  2. Andrew Fiori, Characterization of special points of orthogonal symmetric spaces, J. Algebra 372 (2012), 397-419 Zbl1316.11027MR2990017
  3. S. Garibaldi, A. Rapinchuk, Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C Zbl1285.20045
  4. P. Gille, Type des tores maximaux des groupes semi-simples, J. Ramanujan Math. Soc. 19 (2004), 213-230 Zbl1193.20057MR2139505
  5. T-Y. Lee, Embedding functors and their arithmetic properties Zbl1321.11043
  6. J. Milne, Complex Multiplication 
  7. John Milnor, On isometries of inner product spaces, Invent. Math. 8 (1969), 83-97 Zbl0177.05204MR249519
  8. O. Timothy O’Meara, Introduction to quadratic forms, (2000), Springer-Verlag, Berlin Zbl1034.11003MR1754311
  9. Gopal Prasad, Andrei S. Rapinchuk, Local-global principles for embedding of fields with involution into simple algebras with involution, Comment. Math. Helv. 85 (2010), 583-645 Zbl1223.11047MR2653693
  10. Winfried Scharlau, Quadratic and Hermitian forms, 270 (1985), Springer-Verlag, Berlin Zbl0584.10010MR770063

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