张量三角范畴之间的提升(共)分层

IF 0.8 2区 数学 Q2 MATHEMATICS
Liran Shaul, Jordan Williamson
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引用次数: 0

摘要

我们给出了分层和成本层化沿着R线性张量三角范畴之间的共积保留、张量-act R线性函子下降的必要条件和充分条件,这些R线性张量三角范畴是由它们的张量单元刚性-紧密地生成的。然后,我们将这些结果应用于非正交换 DG 环和连接环谱。特别是,这给出了具有有限振幅的非正换元 DG 环的派生类的(共)定位子类和紧凑对象的厚子类的支持理论分类,并为最终共轭派生方案的关联空间是其底层经典方案这一原理提供了形式上的理由。对于非正交换 DG 环 A,我们还研究了 D(A)中的某些有限性条件(例如代理完备性)是否可以简化为更好理解的类别 D(H0A) 中的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lifting (co)stratifications between tensor triangulated categories

We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact R-linear functor between R-linear tensor-triangulated categories which are rigidly-compactly generated by their tensor units. We then apply these results to non-positive commutative DG-rings and connective ring spectra. In particular, this gives a support-theoretic classification of (co)localizing subcategories, and thick subcategories of compact objects of the derived category of a non-positive commutative DG-ring with finite amplitude, and provides a formal justification for the principle that the space associated to an eventually coconnective derived scheme is its underlying classical scheme. For a non-positive commutative DG-ring A, we also investigate whether certain finiteness conditions in D(A) (for example, proxy-smallness) can be reduced to questions in the better understood category D(H0A).

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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
90
审稿时长
6 months
期刊介绍: The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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