Non-distributive lattices of thick tensor-ideals via trivial extensions
We construct non-rigid tensor-triangulated categories with non-distributive lattice of thick tensor-ideals.
math.CT↗
arXiv subjects
Charalampos Verasdanis
Publications and source records attributed to Charalampos Verasdanis.
The singularity category of a separable extension
We prove that separable extensions of noetherian rings and finite étale morphisms of noetherian schemes give rise to separable extensions of singularity categories.
math.CT↗
Colocalizing subcategories of singularity categories
Utilizing previously established results concerning costratification in relative tensor-triangular geometry, we classify the colocalizing subcategories of the singularity category of a locally hypersurface ring and then we generalize this classification to singularity categories of schemes with hypersurface singularities.
math.CT↗
Costratification and actions of tensor-triangulated categories
We develop the theory of costratification in the setting of relative tensor-triangular geometry, in the sense of Stevenson, providing a unified approach to classification results of Neeman and Benson--Iyengar--Krause, while laying the foundations for future applications. In addition, we introduce and study prime localizing submodules and prime colocalizing $\mathrm{hom}$-submodules, in the first case, generalizing objectwise-prime localizing tensor-ideals. We apply our results to show that the derived category of quasi-coherent sheaves over a noetherian separated scheme is costratified.
math.CT↗
Stratification and the smashing spectrum
We develop the theory of stratification for a rigidly-compactly generated tensor-triangulated category using the smashing spectrum and the small smashing support. Within the stratified context, we investigate connections between big prime ideals, objectwise-prime ideals and homological primes, and we show that the Telescope Conjecture holds if and only if the homological spectrum is $T_0$ and the homological support detects vanishing. We also reduce stratification to smashing localizations. Moreover, we study induced maps between smashing spectra and prove a descent theorem for stratification. Outside the stratified context, we prove that the Telescope Conjecture holds if and only if the smashing spectrum is $T_0$ with respect to the small topology.
math.CT↗