Stratification and the comparison between homological and tensor triangular support
arXiv:2106.16011 · doi:10.1093/qmath/haac040
Abstract
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.
arXiv comment18 pages, comments welcome. v2 - updated to include referee comments. Version to appear in The Quarterly Journal of Mathematics
References in corpus (11)
- Stratifying triangulated categories
- The spectrum of the equivariant stable homotopy category of a finite group
- On the derived category of a graded commutative noetherian ring
- Smashing localizations of rings of weak global dimension at most one
- Nilpotence theorems via homological residue fields
- Tensor-triangular fields: Ruminations
- Homological support of big objects in tensor-triangulated categories
- A thick subcategory theorem for modules over certain ring spectra
- Computing homological residue fields in algebra and topology
- Affine weakly regular tensor triangulated categories
- Support and vanishing for non-Noetherian rings and tensor triangulated categories