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- W4300925260 abstract "Given a $G$-Galois branched cover of the projective line over a number field $K$, we study whether there exists a closed point of $mathbb{P}^1_K$ with a connected fiber such that the $G$-Galois field extension induced by specialization arithmetically descends to $mathbb{Q}$ (i.e., there exists a $G$-Galois field extension of $mathbb{Q}$ whose compositum with the residue field of the point is equal to the specialization). We prove that the answer is frequently positive (whenever $G$ is regularly realizable over $mathbb{Q}$) if one first allows a base change to a finite extension of $K$. If one does not allow base change, we prove that the answer is positive when $G$ is cyclic. Furthermore, we provide an explicit example of a Galois branched cover of $mathbb{P}^1_K$ with no $K$-rational points of arithmetic descent." @default.
- W4300925260 created "2022-10-04" @default.
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- W4300925260 date "2014-12-04" @default.
- W4300925260 modified "2023-10-18" @default.
- W4300925260 title "Arithmetic descent of specializations of Galois covers" @default.
- W4300925260 doi "https://doi.org/10.48550/arxiv.1412.1682" @default.
- W4300925260 hasPublicationYear "2014" @default.
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