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On some splitting properties for algebraic groups over algebraic extensions of global fields

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Abstract

We prove some new Hasse principles related with the property of being split or (strongly) quasi-split for connected smooth affine algebraic groups which are defined over an algebraic extension of a global field. We give also some refinements of the Hasse principles established before for infinite algebraic extensions of global fields.

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Acknowledgements

We thank J. -L. Colliot-Thélène for a discussion while writing Sect. 2.3. We are grateful to the referee for careful reading and for valuable suggestions which help to improve the presentation of the paper.

Funding

This research is partially funded by Vietnam Academy of Science and Technology grant NVCC01.01/23-24 and by the Ministry of Education and Training grant B2022-CTT-01.

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Author notes

  1. Ngô Thị Ngoan and Nguyễn Quốc Th\(\acute{\breve{\textrm{a}}}\)ng have contributed equally to this work.

Authors and Affiliations

  1. Faculty of Mathematical Economics, Thuongmai University, 79 Ho Tung Mau, Cau Giay, Hanoi, 11309, Vietnam

    Ngô Thị Ngoan

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18-Hoang Quoc Viet, Cau Giay, Hanoi, 11307, Vietnam

    Nguyễn Quốc Thắng

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  1. Ngô Thị Ngoan
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  2. Nguyễn Quốc Thắng
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Correspondence to Nguyễn Quốc Thắng.

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Ngoan, N.T., Thắng, N.Q. On some splitting properties for algebraic groups over algebraic extensions of global fields. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01055-x

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