Author
Rössler, D
Journal title
Commentarii Mathematici Helvetici
DOI
10.4171/CMH/344
Issue
1
Volume
90
Last updated
2024-03-21T16:45:39.837+00:00
Page
23-32
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 implies that in some circumstances, the "full" Mordell-Lang conjecture is verified in the situation described above. The proof relies on the theory of semistability (of vector bundles) in positive characteristic and on the existence of the compactification of the universal abelian scheme constructed by Faltings-Chai.
Symplectic ID
745035
Favourite
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Publication type
Journal Article
Publication date
23 Feb 2059
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