A tour about existence and uniqueness of dg enhancements and lifts

By Alberto Canonaco, P. Stellari. 2016

72 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/054dcb9e99d47f608aef959be4b80d91d59d1b21

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In Geometry and Topology

  1. Amnon Yekutieli
  2. Andrei Căldăraru
  3. Michel van den Bergh
  4. Yukinobu Toda
  5. A. Ramadoss
  6. Masaki Kashiwara
  7. James J. Zhang
  8. Wendy Lowen

In Mathematical Physics

  1. Amnon Yekutieli
  2. Andrei Căldăraru
  3. Michel van den Bergh
  4. Yukinobu Toda
  5. A. Ramadoss
  6. Masaki Kashiwara
  7. Damien Calaque
  8. James J. Zhang

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