Abstract.
Recently Anderson described explicitly the epsilon extension of the maximal abelian ℚab of the rational number field ℚ, which is the compositum of all subfield of ℂ quadratic over ℚab and Galois over ℚ. We have given an analogous description of the epsilon extension of the maximal abelian extension of the rational function field over a finite field. In this paper we extend the theory of epsilon extensions partially to a global function field with a distinguished place. The new ingredient is that the base field may have non-trivial class group.
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Received: 31 May 2002 / Revised version: 28 August 2002 Published online: 24 January 2003
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ID="*" Supported by grant No.R01-2002-000-00151-0 from the Basic Research Program of KOSEF.
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ID="**" Supported in part by Distinguished Young Grand in China and BR Program of Tsinghua.
Mathematics Subject Classification (2000): 11R58, 11R20
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Bae, S., Yin, L. Epsilon extensions over global function fields. manuscripta math. 110, 313–324 (2003). https://doi.org/10.1007/s00229-002-0335-3
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DOI: https://doi.org/10.1007/s00229-002-0335-3