Abstract
Let k and K be commutative fields with dimkK=2n, n≥1 and char(k)≠2, 3. If k satisfies one of the following conditions: (1) k is a finite field and k contains a 3-th root of unity, or (2) K is a cyclic extension of k where k is not 3-closed, and k contains a 2a3b-th root of unity, where 6n=2a3bc and c is coprime to 2, 3, then there exists an embedding of the tn-dimensional affine space AG(tn,k) into the t-dimensional affine space AG(t,K), for all t≥2.
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Taniguchi, H. On Embeddings of AG(tn,k) into AG(t,K) with t≥2, n≥1. Geometriae Dedicata 78, 215–228 (1999). https://doi.org/10.1023/A:1005209825174
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DOI: https://doi.org/10.1023/A:1005209825174