Deformation theory of abelian categories

By Wendy Lowen, Michel van den Bergh. 2004

120 citations recorded by the source corpus.

In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the well-known deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations, and we construct several equivalences between deformation problems.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/94e752a4c29e9818acf6a53ab20cd90208df0896

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Michel van den Bergh
2. Wendy Lowen
3. Yukinobu Toda
4. Osamu Iyama
5. Tatiana Gateva-Ivanova
6. Raf Bocklandt
7. Nathan Broomhead
8. Lingyan Guo

In Geometry and Topology

1. Yukinobu Toda
2. Michel van den Bergh
3. Wendy Lowen
4. Emanuele Macrì
5. Arend Bayer
6. P. Stellari
7. D. Huybrechts
8. M. Wemyss

In Mathematical Physics

1. Yukinobu Toda
2. Michel van den Bergh
3. Wendy Lowen
4. Emanuele Macrì
5. Arend Bayer
6. Chunyi Li
7. T. Bridgeland
8. Markus Reineke

Citations in the corpus

• Deformations and Fourier-Mukai transforms (2005, background): “The general deformation theory of Abelian categories was previously studied in [13], and the A∞-deformations of triangulated categories were studied in [1].”
• Hochschild cohomology of abelian categories and ringed spaces (2004, methodology): “For a brief introduction to the theory of universes and to some related terminology which we will use in this paper, we refer the reader to [ 30 ].”
• Definable Additive Categories: Purity and Model Theory (2011, unknown): “It is pointed out in [67] that one may view an S-preadditive category as a non-commutative scheme over the commutative affine base scheme Spec(S).”