Coleman's unramified torsion conjecture for curves with good reduction

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Let p5p\geq 5 be a prime number, and suppose that K/QpK/{\mathbb Q}_p is an unramified finite extension. Let X/KX/K be a curve of genus g2g\geq 2, embedded in its Jacobian via a KK-rational Albanese map. Suppose furthermore that XX has good reduction over KK. A torsion point PX(K)P\in X(\overline{K}) is unramified if its field of definition is unramified over KK. Coleman's conjecture. Every torsion point PX(K)P\in X(\overline{K}) is unramified. This is an open problem concerning the Galois action on torsion points lying on curves embedded in their Jacobians; the stated source presents it as an intriguing open problem and attributes it to R. Coleman.

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Primary source

Matthew Baker and Kenneth A. Ribet, “Galois theory and torsion points on curves”, arXiv:math/0212133 (2002).

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