Adams operations in commutative algebra
Adams operations in commutative algebra
复制标题
交换代数中的 Adams 运算
DOI：
10.1007/978-3-030-65064-3_4
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发表时间：
2021
影响因子：
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通讯作者：
Mark E. Walker
中科院分区：
文献类型：
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作者：
Mark E. Walker
经典的Adams运算定义在概型上的代数向量丛的Grothendieck群上，并与Grothendieck的Riemann-Roch定理有关。在这些笔记中，我回顾了理论的亚当斯业务的Grothendieck集团的支持下，工作的Gillet和Soulé，并给予两个应用在局部代数：证明塞尔消失猜想的任意正则局部环（由于Gillet和Soulé）和证明的总秩猜想的许多地方。
The classicalAdams operationsare defined on the Grothendieck group of algebraic vector bundles on a scheme, and are related to Grothendieck’s Riemann-Roch Theorem. In these notes, I review the theory of Adams operations for Grothendieck groups with supports, following the work of Gillet and Soulé, and give two applications in local algebra: A proof of the Serre Vanishing Conjecture for arbitrary regular local rings (due to Gillet and Soulé) and a proof of the Total Rank Conjecture for many local rings.