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Anabelian geometry of curves over algebraically closed fields of positive characteristic: the case of one-punctured elliptic curves. (English) Zbl 1455.14061

Summary: This article is an announcement of the author’s recent work on anabelian geometry over algebraically closed fields of positive characteristic. We review some known results in this area and give a sketch of the proof of the main result which concerns reconstruction of curves of \((1,1)\)-type by their geometric fundamental groups.

MSC:

14H30 Coverings of curves, fundamental group
14H25 Arithmetic ground fields for curves
14F35 Homotopy theory and fundamental groups in algebraic geometry
14H52 Elliptic curves
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