On the Brauer group of a two-dimensional local field

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• 作者：M. A. Dubovitskaya
• 关键词：two ; dimensional local field ; Brauer group ; field extension ; local field
• 刊名：Mathematical Notes
• 出版年：2007
• 出版时间：June, 2007
• 年：2007
• 卷：81
• 期：5-6
• 页码：753-756
• 全文大小：565 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876

文摘

The two-dimensional local field K = F _q((u))((t)), char K = p, and its Brauer group Br(K) are considered. It is proved that, if L = K(x) is the field extension for which we have x p − x = ut −p =: h, then the condition that (y, f | h]_K = 0 for any y ε K is equivalent to the condition f ε Im(Nm(L*)).