4 citations · 7 across the 9 of their papers we have counts for
10 papers
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…
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…
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…
Definable functors between triangulated categories
Isaac Bird, Jordan Williamson
We systematically develop the theory of definable functors between compactly generated triangulated categories. Such functors preserve pure triangles, pure injective objects, and d…
The homological spectrum via definable subcategories
Isaac Bird, Jordan Williamson
We develop an alternative approach to the homological spectrum of a tensor-triangulated category through the lens of definable subcategories. This culminates in a proof that the ho…
Finitistic dimensions over commutative DG-rings
Isaac Bird, Liran Shaul, Prashanth Sridhar +1
In this paper we study the finitistic dimensions of commutative noetherian non-positive DG-rings with finite amplitude. We prove that any DG-module of finite flat dimension ove…
Duality pairs, phantom maps, and definability in triangulated categories
Isaac Bird, Jordan Williamson
We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine…
Purity, ascent, and periodicity for Gorenstein flat cotorsion modules
Isaac Bird
We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenst…
Cotilting with balanced big Cohen-Macaulay modules
Isaac Bird
Over -dimensional Cohen-Macaulay rings with a canonical module, -cotilting classes containing the maximal and balanced big Cohen-Macaulay modules are classified. Particular e…
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…