Eventually homological isomorphisms in recollements of derived categories
Yongyun Qin

TL;DR
This paper studies conditions under which certain functors in recollements of derived categories become eventually homological isomorphisms, linking algebraic properties like Gorensteinness and Hochschild cohomology.
Contribution
It characterizes when the functor $j^*$ is an eventually homological isomorphism in recollements, connecting algebraic invariants of $A$ and $C$.
Findings
Identifies conditions for $j^*$ to be an eventually homological isomorphism.
Relates Gorensteinness and singularity categories of $A$ and $C$.
Applies results to stratifying ideals, triangular matrix algebras, and derived discrete algebras.
Abstract
For a recollement of derived categories of algebras, we investigate when the functor is an eventually homological isomorphism. In this context, we compare the algebras and with respect to Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology. The results are applied to stratifying ideals, triangular matrix algebras and derived discrete algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
