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We give an elementary self-contained proof of the following result, which Pop proved with methods of rigid geometry.Theorem: Let L 0 /K 0 be a finite Galois extension of complete discrete valued fields.Let t be a transcendental element overThis gives a new proof of the theorem of Fried-Pop-Völklein:Theorem: The absolute Galois group of a countable separably Hilbertian PAC field K is the free profinite group on countably many generators.

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