Abstract
Let K be a global function field of characteristic 2. For each non-trivial place v of K, let \( K_{v} \) be the completion of K at v. We show that if two non-degenerate quadratic forms are similar over every \( K_{v} \), then they are similar over K. This provides an analogue of the version for characteristic not 2 previously obtained by T.Ono.
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Acknowledgements
The author is supported by National Natural Science Foundation of China (No.11701352) and Shantou University Scientific Research Foundation for Talents (No.130-760188). The author thanks Yong Hu for helpful discussions.
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Communicated by Jacques Helmstetter
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Wu, Z. Similarity of Quadratic Forms Over Global Fields in Characteristic 2. Adv. Appl. Clifford Algebras 29, 86 (2019). https://doi.org/10.1007/s00006-019-1006-8
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DOI: https://doi.org/10.1007/s00006-019-1006-8