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On the group of purely inseparable points of an abelian variety defined over a function field of positive characteristic

Abstract:

Let $K$ be the function field of a smooth and proper curve $S$ over an algebraically closed field $k$ of characteristic $p>0$. Let $A$ be an ordinary abelian variety over $K$. Suppose that the N\'eron model $\CA$ of $A$ over $S$ has a closed fibre $\CA_s$, which is an abelian variety of $p$-rank 0. We show that under these assumptions the group $A(K^\perf)/\Tr_{K|k}(A)(k)$ is finitely generated. Here $K^\perf=K^{p^{-\infty}}$ is the maximal purely inseparable extension of $K$. This result ...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/CMH/344

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
Publisher:
Springer
Journal:
Commentarii Mathematici Helvetici More from this journal
Volume:
90
Issue:
1
Pages:
23-32
Publication date:
2015-02-23
DOI:
EISSN:
1420-8946
ISSN:
0010-2571
Keywords:
Pubs id:
pubs:745035
UUID:
uuid:072bbaee-7e33-4e35-b2f8-02f500e9ed17
Local pid:
pubs:745035
Source identifiers:
745035
Deposit date:
2018-04-13

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