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Explicit p-descent for elliptic curves in characteristic p. (English) Zbl 0715.14027
Let K be a function field in one variable over a finite field and E an elliptic curve over K with nonconstant j-invariant. The main result of the paper is that there are only finitely many points in E(K) that are integral at all places of K outside a given finite set of places. The corresponding analogue of Siegel’s theorem for function fields in characteristic zero had been proved by Yu. I. Manin [Transl., Ser. 2, Am. Math. Soc. 50, 127-140 (1966); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 26, 281-292 (1962; Zbl 0103.140)]; the proof here is very similar to Manin’s one once an analogue of the “Manin map” \(E(K)\to K^*\) has been found. This is achieved with the help of explicit formulas for the p-descent on E.
Reviewer: F.Herrlich

MSC:
14H52 Elliptic curves
14G15 Finite ground fields in algebraic geometry
14G05 Rational points
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