对估值域派生类中的粉碎理想进行分类

Scott Balchin, Florian Tecklenburg
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引用次数: 0

摘要

基于巴佐尼-v{S}/v{t}ov\'{/i}/v{c}ek 的结果,我们给出了无限维估值域派生类的粉碎理想框架的完整分类。特别是,我们给出了一个交换环的无穷族的明确构造,使得望远镜猜想失效,并概括了凯勒的一个例子。因此,我们推导出,对于刚性紧凑生成的张量三角范畴,巴尔默谱的克鲁尔维度和粉碎谱的克鲁尔维度可以任意不同。
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Classifying smashing ideals in derived categories of valuation domains
Building on results of Bazzoni-\v{S}\v{t}ov\'{\i}\v{c}ek, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories.
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