On the birational section conjecture with strong birationality assumptions

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2023-09-26 DOI:10.1007/s00222-023-01220-6

Giulio Bresciani

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引用次数: 3

Abstract

Abstract Let $X$ X be a curve over a field $k$ k finitely generated over ℚ and $t$ t an indeterminate. We prove that, if $s$ s is a section of $\pi _{1}(X)\to \operatorname{Gal}(k)$ π 1 ( X ) → Gal ( k ) such that the base change $s_{k(t)}$ s k ( t ) is birationally liftable, then $s$ s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.

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关于具有强血缘假设的血缘截面猜想

摘要设$X$ X是在一个域$k$ k上有限生成的一条曲线，$t$ t是不确定的。我们证明，如果$s$ s是$\pi _{1}(X)\到\operatorname{Gal}(k)$ π 1 (X)→Gal (k)的一个截面，使得基变$s_{k(t)}$ s$ k(t)是双可升的，则$s$ s来自几何。因此，我们证明了截面猜想等价于所有有限生成域上所有截面的离散化。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464