Ramified torsion points on curves. (English) Zbl 0626.14022

The author uses his theory of p-adic integration to prove results about torsion-packets on algebraic curves, i.e. about points, P, Q, in a curve C such that some multiple of the divisor P-Q is principal. The integration theory implies that for any regular differential \(\omega\) the integral of \(\omega\) between P and Q vanishes. If in this integral we vary one of the endpoints we obtain an analytic function on C, and most of the paper deals with properties of this function, especially its zeroes. The final result implies the Manin-Mumford conjecture (which was proved by M. Raynaud).
Reviewer: G.Faltings


14G20 Local ground fields in algebraic geometry
14F30 \(p\)-adic cohomology, crystalline cohomology
14H25 Arithmetic ground fields for curves
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