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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.RT2021
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…
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…