Galois theory over complete local domains |
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Authors: | Elad Paran |
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Institution: | 1. School of Mathematics, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel
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Abstract: | 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. |
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