循环Adams运算
Cyclic Adams Operations
摘要：
设$Q$是交换诺特环，$Z \subseteq \operatorname{Spec}(Q)$是闭子集.定义$K_0^Z(Q)$为在$Z$上有同调支撑的、生成的投射$Q$ -模的有界复形的Grothendieck群。我们在$K_0^Z(Q)$上开发了“循环”Adams运算，并证明这些运算满足Gillet和Soulé在其论文“使用Adams运算的相交理论”中使用的四个公理。从这一点，我们恢复一个较短的证明塞尔的消失猜想。我们还表明，我们的循环亚当斯操作同意亚当斯操作定义的Gillet和Soulé在某些情况下。
英文摘要：
Let $Q$ be a commutative, Noetherian ring and $Z \subseteq \operatorname{Spec}(Q)$ a closed subset. Define $K_0^Z(Q)$ to be the Grothendieck group of those bounded complexes of finitely generated projective $Q$-modules that have homology supported on $Z$. We develop "cyclic" Adams operations on $K_0^Z(Q)$ and we prove these operations satisfy the four axioms used by Gillet and Soulé in their paper "Intersection Theory Using Adams Operations". From this we recover a shorter proof of Serre's Vanishing Conjecture. We also show our cyclic Adams operations agree with the Adams operations defined by Gillet and Soulé in certain cases.
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。
