2021
DOI: 10.2140/akt.2021.6.381
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K-theory and the singularity category of quotient singularities

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Cited by 4 publications
(4 citation statements)
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“…Given a functor which sends to acyclic objects, there is an induced functor (see [GPS20b, § A.7]). We note that the canonical map is a quasi-equivalence, and the canonical map is a Morita equivalence (it is not in general a quasi-equivalence; see [PS21, § 2] for concrete counterexamples).…”
Section: Category Theorymentioning
confidence: 99%
“…Given a functor which sends to acyclic objects, there is an induced functor (see [GPS20b, § A.7]). We note that the canonical map is a quasi-equivalence, and the canonical map is a Morita equivalence (it is not in general a quasi-equivalence; see [PS21, § 2] for concrete counterexamples).…”
Section: Category Theorymentioning
confidence: 99%
“…Of course this relationship should depend on the type of singularities of X. Recall that a variety X over a field of characteristic zero has rational singularities if the derived pushforward R𝜋 * O X coincides with O 𝑋 for some (hence, every) resolution 𝜋 : X → 𝑋. Validity of Conjecture 1.1 does not depend on the choice of a resolution of X, at least in characteristic zero [PS21,Lemma 2.31]. Understanding this conjecture is essential for linking the Minimal Model Program to operations on derived categories, as well as for understanding derived categories of singular varieties.…”
Section: Introductionmentioning
confidence: 99%
“…Recent progress on Conjecture 1.1 includes [Efi20], [BKS18], and [PS21]. Notably, it holds for cones over projectively normal smooth Fano varieties [Efi20]…”
Section: Introductionmentioning
confidence: 99%
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