Uniqueness of enhancement for triangulated categories
Valery A. Lunts,Dmitri Orlov +1 more
TLDR
In this paper, the uniqueness of a DG enhancement for triangulated categories of coherent sheaves and perfect complexes on quasi-projective schemes has been shown for the case of quasi-coherent sheaves.Abstract:
The paper contains general results on the uniqueness of a DG enhancement for trian- gulated categories. As a consequence we obtain such uniqueness for the unbounded categories of quasi-coherent sheaves, for the triangulated categories of perfect complexes, and for the bounded de- rived categories of coherent sheaves on quasi-projective schemes. If a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de- rived categories of coherent sheaves. These results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product.read more
Citations
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Smooth and proper noncommutative schemes and gluing of dg categories
TL;DR: In this paper, it was shown that the world of all geometric noncommutative schemes is closed under an operation of a gluing of differential graded categories via bimodules.
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Categorical resolutions of irrational singularities
TL;DR: In this article, 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.
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The space of stability conditions on the local projective plane
Arend Bayer,Emanuele Macrì +1 more
TL;DR: In this article, the authors study the space of stability conditions on the total space of the canonical bundle over the projective plane and explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component.
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Spherical DG-functors
Rina Anno,Timothy Logvinenko +1 more
TL;DR: In this paper, the authors define the notion of a spherical Morita quasi-functor A -> B and construct its associated autoequivalences: the twist T of D (B) and the co-twist F of D(A).
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Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space
TL;DR: In this paper, the authors prove homological mirror symmetry for a smooth 3-dimensional Calabi-Yau hypersurface in projective space, for any $$d \ge 3-cost σ ≥ 3-Costa (for example, $$d=3-costa is the quintic threefold).
References
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Book
Elements of Algebraic Topology
TL;DR: Elements of Algebraic Topology provides the most concrete approach to the subject with coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorem of point-set topology.
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Des catégories abéliennes
TL;DR: The Bulletin de la S. M. F. as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).