New enhancements of derived categories of coherent sheaves and applications

By V. Lunts, Olaf M. Schnürer. 2014

52 citations recorded by the source corpus.

We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to functors between derived categories of dg algebras, for relating homological smoothness of $Perf(X)$ to geometric smoothness of $X,$ and for proving homological smoothness of $D^b(Coh(X)).$ Moreover, we characterize properness of $Perf(X)$ and $D^b(Coh(X))$ geometrically.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3282dbb93a43e8f820546a5393c6be861e8b67a8

How researchers see this paper

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In Geometry and Topology

1. Alberto Canonaco
2. P. Stellari
3. D. Huybrechts
4. Emanuele Macrì
5. Alexander Kuznetsov
6. Arend Bayer

In Mathematical Physics

1. Alberto Canonaco
2. P. Stellari
3. D. Huybrechts
4. Emanuele Macrì
5. Alexander Kuznetsov
6. Arend Bayer

Citations in the corpus

• A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “A complete argument has been recently provided in [42], under more general assumptions than the ones in this paper (see also [56]).”