Geodesic
On the homotopy finiteness of DG categories
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 3, pp. 431-460

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This paper gives a short overview of results related to homotopy finiteness of DG categories. A general plan is explained for proving homotopy finiteness of derived categories of coherent sheaves and coherent matrix factorizations on separated schemes of finite type over a field of characteristic zero. Bibliography: 39 titles.
Keywords: derived categories, differential graded categories, homotopy finiteness, Verdier localization, resolution of singularities. 
A. I. Efimov. On the homotopy finiteness of DG categories. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 3, pp. 431-460. http://geodesic.mathdoc.fr/item/RM_2019_74_3_a2/
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