Gersten猜想的一个奇异模拟及其在K-理论adeles中的应用
A singular analogue of Gersten's conjecture and applications to K-theoretic adeles
摘要：
本文的第一部分介绍了Gersten关于离散赋值环的内射性猜想在一维奇异完全局部环上的一个类似。我们的主要定理是当环是约化的且包含Q时，利用循环/霍赫希尔德同调和A.克里希纳本文的第二部分描述了K-理论的阿黛尔型决议之间的关系在一个一维的计划和更经典的问题在K-理论，如本地化和下降。特别地，我们构造了一个新的决议的层化K-理论，条件的猜想。
英文摘要：
The first part of this paper introduces an analogue, for one-dimensional, singular, complete local rings, of Gersten's injectivity conjecture for discrete valuation rings. Our main theorem is the verification of this conjecture when the ring is reduced and contains Q, using methods from cyclic/Hochschild homology and Artin-Rees type results due to A. Krishna. The second part of the paper describes the relationship between adele type resolutions of K-theory on a one-dimensional scheme and more classical questions in K-theory such as localisation and descent. In particular, we construct a new resolution of sheafified K-theory, conditionally upon the conjecture.
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