Coleman's unramified torsion conjecture for curves with good reduction
Coleman's unramified torsion conjecture for curves with good reduction
Let be a prime number, and suppose that is an unramified finite extension. Let be a curve of genus , embedded in its Jacobian via a -rational Albanese map. Suppose furthermore that has good reduction over . A torsion point is unramified if its field of definition is unramified over . Coleman's conjecture. Every torsion point 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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Sources & referencesView supporting material
Primary source
Matthew Baker and Kenneth A. Ribet, “Galois theory and torsion points on curves”, arXiv:math/0212133 (2002).
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