Abstract
Let ๐ be a non-perfect separably closed field.
Let ๐บ be a connected reductive algebraic group defined over ๐.
We study rationality problems for Serreโs notion of complete reducibility of subgroups of ๐บ.
In particular, we present the first example of a connected non-abelian ๐-subgroup ๐ป of ๐บ that is ๐บ-completely reducible but not ๐บ-completely reducible over ๐, and the first example of a connected non-abelian ๐-subgroup
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 19K14516
Funding statement: While undertaking the work for this article, the second and third authors were supported by Alexander von Humboldt Fellowships. The third author also acknowledges the financial support of JSPS Grant-in-Aid for Early-Career Scientists (19K14516).
Acknowledgements
The authors would like to thank Gerhard Rรถhrle and Michael Bate for helpful comments.
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Communicated by: Timothy C. Burness
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