Smooth compactifications of certain normic bundles

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• 作者：Anthony Várilly-Alvarado ; Bianca Viray
• 关键词：Normic bundles ; Hasse principle ; Smooth compactifications ; Brauer–Manin obstruction ; 11G35 ; 14G05
• 刊名：European Journal of Mathematics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：1
• 期：2
• 页码：250-259
• 全文大小：411KB
• 参考文献：1.Artin, M.: Left ideals in maximal orders. In: Brauer Groups in Ring Theory and Algebraic Geometry (Wilrijk, 1981). Lecture Notes in Mathematics, vol. 917, pp. 182-93. Springer, Berlin (1982)
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• 作者单位：Anthony Várilly-Alvarado (1)
  Bianca Viray (2)
  
  1. Department of Mathematics, Rice University, 6100 S. Main St. MS 136, Houston, TX, 77005, USA
  2. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA
  
• 刊物类别：Algebraic Geometry;
• 刊物主题：Algebraic Geometry;
• 出版者：Springer International Publishing
• ISSN：2199-6768

文摘

For a finite cyclic Galois extension of fields \(K/k\) of degree \(n\) and a separable polynomial of degree \(dn\) or \(dn - 1\), we construct an explicit smooth compactification \(X \rightarrow {\mathbb P}^1_k\) of the affine normic bundle \(X_0\) given by $$\begin{aligned} {{\mathrm{N}}}_{K/k}(\mathbf {z}) = P(x) \ne 0, \end{aligned}$$