Stratification and the comparison between homological and tensor triangular support
Stratification and the comparison between homological and tensor triangular support
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DOI：
10.1093/qmath/haac040
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发表时间：
2021-06
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通讯作者：
T. Barthel;Drew Heard;Beren Sanders
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作者：
T. Barthel;Drew Heard;Beren Sanders
我们比较了刚性紧生成的张量三角范畴中的“大”对象的同调支撑和张量三角支撑。我们证明了从同调谱到张量三角谱的比较映射是一个双射，并且当范畴是分层的时，这两个支持的概念是一致的，扩展了Balmer的工作。此外，我们澄清的支持函数的显着性质之间的关系，并展示反例突出同调和张量三角支持之间的差异。
We compare the homological support and tensor triangular support for `big' objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the homological spectrum to the tensor triangular spectrum is a bijection and that the two notions of support coincide whenever the category is stratified, extending work of Balmer. Moreover, we clarify the relations between salient properties of support functions and exhibit counter-examples highlighting the differences between homological and tensor triangular support.