Refined class number formulas for elliptic units

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• 作者：C. Gomez
• 关键词：Euler systems ; Kolyvagin systems ; Primary 11R29 ; Secondary 11R04 ; 11R11 ; 11R18 ; 11R27
• 刊名：Annales math篓娄matiques du Qu篓娄bec
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：39
• 期：1
• 页码：1-24
• 全文大小：580 KB
• 参考文献：1.Darmon, H.: Thaine’s method for circular units and a conjecture of Gross. Canad. J. Math. 47, 302-17 (1995)MathSciNet View Article
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  4.Mazur, B., Rubin, K.: Refined class number formulas and Kolyvagin systems. Compos. Math. 147, 56-4 (2011)MathSciNet View Article
  5.Mazur, B., Tate, J.: Refined conjectures of the Birch and Swinnerton-Dyer type. Duke Math. J. 54(2), 711 (1987)MathSciNet View Article
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  7.Rubin, K.: Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer in Arithmetic Theory of Elliptic Curves. Lectures Notes in Mathematics 1716, 167-34 (1997)
  8.Serre, J.-P.: Corps locaux. 4e édition Hermann, Paris (1968)
  9.Siegel, C.L.: On advanced analytic number theory. Tata Institute of Fundamental Research, Mumbai, India (1965)
  
• 作者单位：C. Gomez (1)
  
  1. Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada
  
• 刊物主题：Number Theory; Algebra; Analysis;
• 出版者：Springer International Publishing
• ISSN：2195-4763

文摘

We generalize the notions of Kolyvagin and pre-Kolyvagin systems to prove “refined class number formulas-for quadratic extensions of a quadratic imaginary fields \(K\) of class number one. Our main result generalises the results and conjectures of Darmon (Canad. J. Math. 47:302-17, 1995), by replacing circular units in abelian extensions of \(\mathbb {Q}\) by elliptic units in abelian extensions of K.