A remark on local-global principles for conjugacy classes

Yuval Z. Flicker Department of Mathematics, Ohio State University

TBD mathscidoc:1701.332973

Arkiv for Matematik, 40, (1), 47-53, 2000.9
A local-global principle is shown to hold for all conjugacy classes of any inner form of GL($n$), SL($n$), U($n$), SU($n$), and for all semisimple conjugacy classes in any inner form of Sp($n$), over fields$k$with vcd($k$)≤1. Over number fields such a principle is known to hold for any inner form of GL($n$) and U($n$), and for the split forms of Sp($n$), O($n$), as well as for SL($p$) but not for SL($n$),$n$non-prime. The principle holds for all conjugacy classes in any inner form of GL($n$), but not even for semisimple conjugacy classes in Sp($n$), over fields$k$with vcd($k$)≤2. The principle for conjugacy classes is related to that for centralizers.
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@inproceedings{yuval2000a,
  title={A remark on local-global principles for conjugacy classes},
  author={Yuval Z. Flicker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603494302782},
  booktitle={Arkiv for Matematik},
  volume={40},
  number={1},
  pages={47-53},
  year={2000},
}
Yuval Z. Flicker. A remark on local-global principles for conjugacy classes. 2000. Vol. 40. In Arkiv for Matematik. pp.47-53. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203603494302782.
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