论文标题
纯粹是不可分割的richelot isent
Purely inseparable Richelot isogenies
论文作者
论文摘要
我们表明，如果$ c $是一个超属属 - $ 2 $曲线，而$ 2 $ $ 2 $，那么从$ c $开始，有无限的Richelot Isogenies。这与特征性$ 2 $的非s弹性曲线或特征性曲线而不是$ 2 $相反：在这些情况下，最多有15个Richelot Isgenies从给定的属-2 $ 2 $曲线开始。 More specifically, we show that if $C_1$ and $C_2$ are two arbitrary supersingular genus-$2$ curves over an algebraically-closed field of characteristic $2$, then there are exactly sixty Richelot isogenies from $C_1$ to $C_2$, unless either $C_1$ or $C_2$ is isomorphic to the curve $y^2 + y = x^5$.在这种情况下，根据$ C_1 $的$ C_1 $从$ C_1 $到$ C_1 $是同构至$ C_2 $的十二或四个Richelot Isenies。 （在这里，我们将Richelot的同源性计算为同构。）我们给出了明确的构造，这些结构在两个超顺曲线之间产生所有Richelot isenente。
We show that if $C$ is a supersingular genus-$2$ curve over an algebraically-closed field of characteristic $2$, then there are infinitely many Richelot isogenies starting from $C$. This is in contrast to what happens with non-supersingular curves in characteristic $2$, or to arbitrary curves in characteristic not $2$: In these situations, there are at most fifteen Richelot isogenies starting from a given genus-$2$ curve. More specifically, we show that if $C_1$ and $C_2$ are two arbitrary supersingular genus-$2$ curves over an algebraically-closed field of characteristic $2$, then there are exactly sixty Richelot isogenies from $C_1$ to $C_2$, unless either $C_1$ or $C_2$ is isomorphic to the curve $y^2 + y = x^5$. In that case, there are either twelve or four Richelot isogenies from $C_1$ to $C_2$, depending on whether $C_1$ is isomorphic to $C_2$. (Here we count Richelot isogenies up to isomorphism.) We give explicit constructions that produce all of the Richelot isogenies between two supersingular curves.
