Author
Gillet, H
Rössler, D
Journal title
Mathematische Annalen
Last updated
2024-03-27T07:10:21.657+00:00
Abstract
Let $K$ be the function field of a smooth curve over an algebraically closed
field $k$. Let $X$ be a scheme, which is smooth and projective over $K$.
Suppose that the cotangent bundle $\Omega_{X/K}$ is ample. Let $R:={\rm
Zar}(X)(K)\cap X)$ be the Zariski closure of the set of all $K$-rational points
of $X$, endowed with its reduced induced structure. We prove that there is a
projective variety $X_0$ over $k$ and a finite and surjective $K^{\rm
sep}$-morphism $X_{0,K^{\rm sep}}\to R_{K^{\rm sep}}$, which is birational when
${\rm char}(K)=0$.
Symplectic ID
745063
Download URL
http://arxiv.org/abs/1312.6008v3
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Publication type
Journal Article
Publication date
01 Jun 2018
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