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Uspekhi Mat. Nauk, 2019, Volume 74, Issue 3(447), Pages 63–94 (Mi umn9887)  

On the homotopy finiteness of DG categories

A. I. Efimovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b National Research University Higher School of Economics

Abstract: 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
This work was supported by the Laboratory of Mirror Symmetry, National Research University Higher School of Economics (Russian Federation government grant, ag. no. 14.641.31.0001).


DOI: https://doi.org/10.4213/rm9887

Full text: PDF file (705 kB)
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English version:
Russian Mathematical Surveys, 2019, 74:3, 431–460

Bibliographic databases:

UDC: 512.7
MSC: 14E05, 18E30, 18E35
Received: 01.04.2019

Citation: A. I. Efimov, “On the homotopy finiteness of DG categories”, Uspekhi Mat. Nauk, 74:3(447) (2019), 63–94; Russian Math. Surveys, 74:3 (2019), 431–460

Citation in format AMSBIB
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