Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.
The category $\big[{\mathcal T}^c\big]^{\text{op}}$ as functors on ${\mathcal T}^b_c$
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abstract
We revisit an old assertion due to Rouquier, characterizing the perfect complexes as bounded homological functors on the bounded complexes of coherent sheaves. The new results vastly generalize the old statement---first of all the ground ring is not restricted to be a field, any commutative, noetherian ring will do. But the generalization goes further, to the abstract world of approximable triangulated categories.
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2024 1verdicts
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Deformations of triangulated categories with t-structures via derived injectives
Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.