Submission date: 30 November 2012.

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 Néron 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, as well as a conjecture of Esnault and Langer, are verified.

Mathematics Subject Classification: 14K99

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Full text arXiv 1211.6943: pdf, ps.