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The singularity category via the stabilization
Xiao-Wu Chen
We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The resu…
Noncommutative Knörrer periodicity via equivariantization
Xiao-Wu Chen, Wenchao Wu
We establish noncommutative Knörrer periodicity for projective-module factorizations over an arbitrary ring, using the equivariantization theory with respect to various actions by…
The singularity category as a stable module category
Xiao-Wu Chen, Zhengfang Wang
We investigate the stabilization of the module category over an artinian ring by formally inverting the tensor endofunctor given by the bimodule of relative nonco…
Higher-dimensional module factorizations and complete intersections
Xiao-Wu Chen
We introduce higher-dimensional module factorizations associated to a regular sequence. They include higher-dimensional matrix factorizations, which are commutative cubes consistin…