通过可定义的子范畴的同调谱

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-07 DOI:10.1112/blms.70014

Isaac Bird, Jordan Williamson

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引用次数: 0

摘要

我们通过可定义子范畴的视角，为张量三角范畴的同调谱开发了另一种方法。最终，我们证明了同调谱与齐格勒谱的商同构。在此过程中，我们根据与给定同素对应的可定义子类，描述了同素残差域中的注入对象。我们利用这些结果从纯粹性的角度探讨了同调谱与巴尔默谱之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The homological spectrum via definable subcategories

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The homological spectrum via definable subcategories

We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the homological spectrum is homeomorphic to a quotient of the Ziegler spectrum. Along the way, we characterise injective objects in homological residue fields in terms of the definable subcategory corresponding to a given homological prime. We use these results to give a purity perspective on the relationship between the homological and Balmer spectrum.

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