3 papers
math.CT2025
Definable functoriality of tensor-triangular spectra
Isaac Bird, Jordan Williamson
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functor…
math.CT2025
Duality in tensor-triangular geometry via proxy-smallness
Thomas Peirce, Jordan Williamson
We make a systematic study of duality phenomena in tensor-triangular geometry, generalising and complementing previous results of Balmer--Dell'Ambrogio--Sanders and Dwyer--Greenlee…
math.CT2025
The shift-homological spectrum and parametrising kernels of rank functions
Isaac Bird, Jordan Williamson, Alexandra Zvonareva
For any compactly generated triangulated category we introduce two topological spaces, the shift-spectrum and the shift-homological spectrum. We use them to parametrise a family of…