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- W2034454460 abstract "Let $X$ be a Berkovich space over a valued field. We prove that every finite group is a Galois group over $Ms(B)(T)$, where $Ms(B)$ 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 ${bf Z}$ and use a similar strategy to give a new proof of the following theorem by D. Harbater: every finite group is a Galois group over a field of convergent arithmetic power series. We believe our proof to be more geometric and elementary that the original one. We have included the necessary background on Berkovich spaces over ${bf Z}$." @default.
- W2034454460 created "2016-06-24" @default.
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- W2034454460 date "2010-02-05" @default.
- W2034454460 modified "2023-09-26" @default.
- W2034454460 title "Raccord sur les espaces de Berkovich" @default.
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- W2034454460 doi "https://doi.org/10.2140/ant.2010.4.297" @default.
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