
ON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASEON RAMIFIED TORSION POINTS ON A CURVE WITH STABLE REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASEAA00765910 
"/Hoshi, Yuichiro/"Hoshi, Yuichiro
54
(
4
)
, pp.767

787 , 201710 , Osaka University and Osaka City University, Departments of Mathematics
ISSN:00306126
NCID:AA00765910
Description
Let p be an odd prime number, W an absolutely unramified padically complete discrete valuation ring with algebraically closed residue field, and X a curve of genus at least two over the field of fractions K of W. In the present paper, we study, under the assumption that X has stable reduction over W, torsion points on X, i.e., torsion points of the Jacobian variety J of X which lie on the image of the Albanese embedding X → J with respect to a Krational point of X. A consequence of the main result of the present paper is that if, moreover, J has good reduction over W, then every torsion point on X is Krational after multiplying p. This result is closely related to a conjecture of R. Coleman concerning the ramification of torsion points. For instance, this result leads us to a solution of the conjecture in the case where a given curve is hyperelliptic and of genus at least p.
FullText
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