集合论意义下的完美理想与剩余交
Set-Theoretically Perfect Ideals and Residual Intersections
AI总结：
本文研究满足Serre条件Sₛ环中的代数剩余交，证明其存在自由逼近（即具相同根的完美子理想），由此确定剩余交重数的一致上界；在正特征下，剩余交是上同调完全交，故其簇在余维1连通。
摘要：
本文研究满足Serre条件\
英文摘要：
This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a uniform upper bound for the multiplicity of residual intersections. In positive characteristic, it follows that residual intersections are cohomologically complete intersection and, hence, their variety is connected in codimension one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
