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arXiv · 1406.7559

New enhancements of derived categories of coherent sheaves and applications

Valery A. Lunts·Olaf M. Schnürer
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Abstract

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.

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Valery A. Lunts, Olaf M. Schnürer. 2014-06-29. New enhancements of derived categories of coherent sheaves and applications. https://arxiv.org/abs/1406.7559

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