Equivariant epsilon constant conjectures for weakly ramified extensions

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• 作者：Werner Bley ; Alessandro Cobbe
• 刊名：Mathematische Zeitschrift
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：283
• 期：3-4
• 页码：1217-1244
• 全文大小：650 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823
• 卷排序：283

文摘

We study the local epsilon constant conjecture as formulated by Breuning in Breuning (J London Math Soc 70(2):289–306, 2004). This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected compatibility of the ETNC with the functional equation of Artin-L-functions. Let \(K/\mathbb {Q}_p\) be unramified. Under some mild technical assumption we prove Breuning’s conjecture for weakly ramified abelian extensions N / K with cyclic ramification group. As a consequence of Breuning’s local-global principle we obtain the validity of the global epsilon constant conjecture as formulated in Bley and Burns (Proc Lond Math Soc 87(3):545–590, 2003) and of Chinburg’s \(\Omega (2)\)-conjecture as stated in Chinburg (Ann Math 121(2):351–376, 1985) for certain infinite families F / E of weakly and wildly ramified extensions of number fields.KeywordsLocal epsilon constant conjecturesEquivariant Tamagawa number conjectureWeak ramification