Categorical resolutions of irrational singularities

By Alexander Kuznetsov, V. Lunts. 2012

128 citations recorded by the source corpus.

We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8de1e66643eb3182c4534214ddcdcdc1a0772586

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In Geometry and Topology

1. A. Neeman
2. J. Št’ovíček
3. Henning Krause
4. James Gillespie
5. Manuel Saor'in
6. Moritz Groth

In Mathematical Physics

1. A. Neeman
2. J. Št’ovíček
3. Henning Krause
4. James Gillespie
5. Manuel Saor'in
6. Moritz Groth

Citations in the corpus

• Non-commutative resolutions of quotient singularities for reductive groups (2015, unknown): “Then the functor D(S)→ D( ) : N → M L ⊗S N is fully faithful and hence yields a categorical resolution of singularities of S in the sense of [33,35,42].”
• Strong generators in $D^{perf}(X)$ and $D^b_{coh}(X)$ (2017, methodology): “es of (i). There are the ones that come from (ii) and (iv). And then we can produce more examples by forming admissible subcategories as in (iii) and using the gluing procedure of Kuznetsov and Lunts [19] sketched above. 6 AMNON NEEMAN If the underlying commutative ring R is a perfect field then any ”