A tour about existence and uniqueness of dg enhancements and lifts

JOURNAL OF GEOMETRY AND PHYSICS

卷:122

Article; Proceedings Paper

Canonaco, Alberto¹  Stellari, Paolo² 

[1] Univ Pavia, Dipartimento Matemat F Casorati, Via Ferrata 5, I-27100 Pavia, Italy

[2] Univ Milan, Dipartimento Matemat F Enriques, Via Cesare Saldini 50, I-20133 Milan, Italy

关键词: Dg categories;    Dg enhancements;    Triangulated categories;   

DOI  :  10.1016/j.geomphys.2016.11.030

来源: Elsevier

【 摘 要 】

This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulated categories arising in algebraic geometry have a unique dg enhancement. This is the case, for example, for the unbounded derived category of quasi-coherent sheaves on an algebraic stack or for its full triangulated subcategory of perfect complexes. Moreover we give an account of the recent results about the possibility to lift exact functors between the bounded derived categories of coherent sheaves on smooth schemes to dg (quasi-)functors. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free