Ramification of torsion points on a curve with superspecial reduction over an absolutely unramified base

Abstract

— Let p be a prime number, W an absolutely unramified p-adically complete discrete valuation ring with algebraically closed residue field, and X a curve over the field of fractions of W of genus greater than one. In the present paper, we study the ramification of torsion points on the curve X. A consequence of the main result of the present paper is no existence of ramified torsion point on X in the case where p is greater than three, the Jacobian variety J of X has good reduction over W , and the special fiber of the good model of J is superspecial. This consequence generalizes a theorem proved by Coleman.