Abstract
A. Huber and B. Kahn construct a relative slice filtration on the motive M(X) associated to a principal T-bundle \(X\rightarrow Y\) for a smooth scheme Y. As a consequence of their result, one can observe that the mixed Tateness of the motive M(Y) implies that the motive M(X) is mixed Tate. In this note we prove the inverse implication for a principal G-bundle, for a split reductive group G.
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Acknowledgements
The first author warmly thanks B. Kahn for very useful comments on the earlier draft of the paper. She thanks J. Ayoub and E. Arasteh Rad for useful comments and discussions. She is also grateful to Prof. Luca Barbieri Viale for steady encouragement. This research was in part supported by a grant from IPM (No. 1402140032).
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Communicated by S. Mohammad Hadi Hedayatzadeh.
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Habibi, S., Rahmati, F. A Remark on a Result of Huber and Kahn. Bull. Iran. Math. Soc. 50, 18 (2024). https://doi.org/10.1007/s41980-024-00861-4
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DOI: https://doi.org/10.1007/s41980-024-00861-4