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Raccord sur les espaces de Berkovich

2010
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Algebra & Number Theory
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Let X be a Berkovich space over a valued field. We prove that every finite group is a Galois group over (B)(T), where (B) is the field of meromorphic functions over a part B of X satisfying some conditions. This gives a new geometric proof that every finite group is a Galois group over K(T), where K is a complete valued field with non-trivial valuation. Then we switch to Berkovich spaces over Z and use a similar strategy to give a new proof of the following theorem by D. Harbater: every finite

doi:10.2140/ant.2010.4.297
fatcat:sxitgtvr3rg75ltxtxz3uy627u