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Computing Torsion Points on Curves

2001
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Experimental Mathematics
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Let X be a curve of genus g ≥ 2 over a field k of characteristic zero. Let X → A be an Albanese map associated to a point P 0 on X. The Manin-Mumford conjecture, first proved by Raynaud, asserts that the set T of points in X(k) mapping to torsion points on A is finite. Using a p-adic approach, we develop an algorithm to compute T , and implement it in the case where k = Q, g = 2, and P 0 is a Weierstrass point. Improved bounds on #T are also proved: for instance, in the context of the previous

doi:10.1080/10586458.2001.10504462
fatcat:2tdcqojqajeyzoer6juom5vpte