3 papers
math.RT2026
Definable functors and Brown--Adams representability
Isaac Bird
The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable fun…
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…
math.RT2019
Two definable subcategories of maximal Cohen-Macaulay modules
Isaac Bird
Over a Cohen-Macaulay ring we consider two extensions of the maximal Cohen-Macaulay modules from the viewpoint of definable subcategories, which are closed under direct limits, dir…