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European Journal of Mathematics

, Volume 3, Issue 2, pp 311–341 | Cite as

Minors and resolutions of non-commutative schemes

  • Igor Burban
  • Yuriy DrozdEmail author
  • Volodymyr Gavran
Research Article

Abstract

We develop the theory of minors of non-commutative schemes. This study is motivated by applications in the theory of non-commutative resolutions of singularities of commutative schemes. In particular, we construct a categorical resolution for non-commutative curves and in the rational case show that it can be realized as the derived category of a quasi-hereditary algebra.

Keywords

Derived categories Bilocalization Non-commutative schemes Minors 

Mathematics Subject Classification

14F05 14A22 

Notes

Acknowledgements

The results of this paper were mainly obtained during the stay of the second author at the Max-Plank-Institut für Mathematik. Its final version was prepared during the visit of the second and the third author to the Institute of Mathematics of the Köln University.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnCologneGermany
  2. 2.Institute of MathematicsNational Academy of Sciences of UkraineKievUkraine

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