发表机构
Tongji University（同济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在含本原p次单位根的数域上，借助类群的p挠子群界定超椭圆雅可比簇相关Selmer群的范围，并辅以实例说明结果。
AI 中文摘要
设K为包含本原p次单位根ζₚ的数域，f(x)∈K[x]为首一整系数多项式，f₀表示其根基，C/K为由yᵖ=f(x)定义的超椭圆曲线，J为其雅可比簇。簇J在K上允许ζₚ乘法，特别地，由Π:=1−ζₚ诱导的自同态给出K上J的一个同源。设Sel_Π(J)为与Π关联的Selmer群，在适当假设下，我们根据L:=K[x]/(f₀)的类群的p挠子群得到Sel_Π(J)的界，还讨论了若干说明该结果的例子。
英文摘要
Let $K$ be a number field containing a primitive $p$-th root of unity $ζ_p$. Let $f(x)\in K[x]$ be a monic integral polynomial, and let $f_0$ denote its radical. Let $C/K$ be the superelliptic curve defined by $y^p=f(x)$, and let $J$ be its Jacobian variety. The variety $J$ admits multiplication by $ζ_p$ over $K$; in particular, the endomorphism induced by $Π:=1-ζ_p$ gives an isogeny of $J$ over $K$. Let $\operatorname{Sel}_Π(J)$ denote the Selmer group associated to $Π$. Under suitable hypotheses, we obtain bounds for $\operatorname{Sel}_Π(J)$ in terms of the $p$-torsion subgroup of the class group of $L:=K[x]/(f_0)$. Several examples illustrating the results are also discussed.
Comments19 pages
