Abstract
Let k be a field, and let L be an étale k-algebra of finite rank. If \(a \in {k^ \times }\), let Xa be the affine variety defined by \({N_{L/k}}(x) = a\). Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial description of the unramified Brauer group of Xa.
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Dedicated to Moshe Jarden for his 80th birthday
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Bayer-Fluckiger, E., Lee, TY. Norm tori of étale algebras and unramified Brauer groups. Isr. J. Math. 257, 3–25 (2023). https://doi.org/10.1007/s11856-023-2533-5
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DOI: https://doi.org/10.1007/s11856-023-2533-5