Problem 836

A Bold Proposition

Let $A$ be an affine plane over a radically integral local field $F$ with residual characteristic $p$.

We consider an open oriented line section $U$ of $A$ with normalized Haar measure $m$.

Define $f(m, p)$ as the maximal possible discriminant of the jacobian associated to the orthogonal kernel embedding of $U$ into $A$.

Find $f(20230401, 57)$. Give as your answer the concatenation of the first letters of each bolded word.

考虑仿射平面(affine plane)$A$，定义在根式积分局部域(radically integral local field)$F$上，其剩余特征值为$p$。

考虑$A$的一个开有向直线截面(open oriented line section)$U$，其正规化哈尔测度为$m$。

定义$f(m, p)$为特定雅各比矩阵(jacobian)的判别式的最大值，该矩阵对应于$U$对$A$的正交核嵌入(orthogonal kernel embedding)。

求$f(20230401, 57)$，并将本文中所有加粗单词的首字母连起来作为你的答案。

译注：愚人节快乐！