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We prove that one can realize certain triangulated subcategories of thesingularity category of a complete intersection as homotopy categories ofmatrix factorizations. Moreover, we prove that for any commutative ring andnon-zerodivisor, the homotopy category of matrix factorizations embeds into thehomotopy category of totally acyclic complexes of finitely generated projectivemodules over the factor ring.

Complete intersections and equivalences with categories of matrix factorizations