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Rational points of varieties with ample cotangent bundle over function fields of positive characteristic

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 ${\rm char}(K)=0$.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00208-017-1569-4

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer Berlin Heidelberg
Journal:
Mathematische Annalen More from this journal
Volume:
371
Issue:
3-4
Pages:
1137–1162
Publication date:
2017-07-19
Acceptance date:
2017-06-25
DOI:
EISSN:
1432-1807
ISSN:
0025-5831
Keywords:
Pubs id:
pubs:745063
UUID:
uuid:27dcd487-1cac-4e6f-8f6a-935d30646bba
Local pid:
pubs:745063
Source identifiers:
745063
Deposit date:
2017-11-11

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