Galois theory over complete local domains

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Complete local domains play an important role in commutative algebra and algebraic geometry, and their algebraic properties were already described by Cohen's structure theorem in 1946. However, the Galois theoretic properties of their quotient fields only recently began to unfold. In 2005 Harbater and Stevenson considered the two dimensional case. They proved that the absolute Galois group of the field K((X, Y)) (where K is an arbitrary field) is semi-free. In this work we settle the general case, and prove that if R is a complete local domain of dimension exceeding 1, then the quotient field of R has a semi-free absolute Galois group.

Original languageEnglish
Pages (from-to)395-413
Number of pages19
JournalMathematische Annalen
Issue number2
StatePublished - 2010
Externally publishedYes

Bibliographical note

Funding Information:
Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation, and by the GTEM network.


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