AI 中文总结
本文研究奇剩余特征完全离散赋值域上椭圆曲线的整2-adic Tate模，利用显式对半公式确定伽罗瓦群在2幂挠塔的作用，证明其由2-挠表示、c的平方类及根差的局部信息决定。
AI 中文摘要
我们证明，奇剩余特征的完全离散赋值域上椭圆曲线的整2-adic Tate模，由其2-挠表示、c的平方类，以及模型E∶y²=cf(x)中f（首一三次多项式）的根两两差的局部信息共同决定。证明采用显式对半公式确定伽罗瓦群在整个2幂挠塔上的作用。
英文摘要
We show that the integral $2$-adic Tate module of an elliptic curve over a complete discretely valued field of odd residue characteristic is determined by its $2$-torsion representation, together with the square class of $c$ and local information about the pairwise differences of the roots of $f$ in a model $E\colon y^2=cf(x)$, where $f$ is monic of degree $3$. The proof uses explicit halving formulae to determine the Galois action on the full tower of $2$-power torsion.
Comments7 pages. Comments welcome!
