Stratification and the comparison between homological and tensor triangular support
Tobias Barthel, Drew Heard, Beren Sanders
Abstract
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 the 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.
Topics & Concepts
BijectionMathematicsTensor (intrinsic definition)Pure mathematicsSalientBalmer seriesAlgebra over a fieldCombinatoricsComputer scienceArtificial intelligenceSpectral linePhysicsAstronomyEmission spectrumAlgebraic structures and combinatorial modelsHomotopy and Cohomology in Algebraic TopologyTopological and Geometric Data Analysis