manuscripta mathematica

, Volume 110, Issue 3, pp 313–324 | Cite as

Epsilon extensions over global function fields

  • Sunghan Bae
  • Linsheng Yin


 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.


Rational Function Rational Number Class Group Finite Field Function Field 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sunghan Bae
    • 1
  • Linsheng Yin
    • 2
  1. 1.Department of Mathematics, KAIST, Taejon 305-701, Korea. e-mail: shbae@
  2. 2.Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China. e-mail:

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