# Homotopy finiteness of some DG categories from algebraic geometry

@article{Efimov2013HomotopyFO, title={Homotopy finiteness of some DG categories from algebraic geometry}, author={Alexander I. Efimov}, journal={arXiv: Algebraic Geometry}, year={2013} }

In this paper, we prove that the bounded derived category $D^b_{coh}(Y)$ of coherent sheaves on a separated scheme $Y$ of finite type over a field $\mathrm{k}$ of characteristic zero is homotopically finitely presented. This confirms a conjecture of Kontsevich. We actually prove a stronger statement: $D^b_{coh}(Y)$ is equivalent to a DG quotient $D^b_{coh}(\tilde{Y})/T,$ where $\tilde{Y}$ is some smooth and proper variety, and the subcategory $T$ is generated by a single object.
The proof uses…

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