Tohoku Mathematical Journal
2022
December
SECOND SERIES VOL. 74, NO. 4

Tohoku Math. J.
74 (2022), 521-534

Title RAMIFICATION OF TORSION POINTS ON A CURVE WITH SUPERSPECIAL REDUCTION OVER AN ABSOLUTELY UNRAMIFIED BASE

Author Yuichiro Hoshi

(Received June 18, 2020, revised June 3, 2021)
Abstract. Let $p$ be a prime number, $W$ an absolutely unramified $p$-adically complete discrete valuation ring with perfect 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 nonexistence 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.

Mathematics Subject Classification. Primary 14H25; Secondary 11G20, 14H40, 14L15.
Key words and phrases. Curve, ramified torsion point, superspecial.

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