A guiding principle of non-commutative algebraic geometry is that geometric objects (i.e. rings and schemes) are replaced by categories of modules/sheaves thereof. In order to keep track of the homological information, we actually take derived categories of such modules/sheaves. From this point of view, we are now interested in understanding typical geometric concepts directly in this categorical framework. A key example is given by deformations. In this talk, I will report on joint work with W. Lowen and M. Van den Bergh, where we attempt to define and study deformations categorically, in the framework of (enhanced) triangulated categories with a t-structure. This will also shed light on Hochschild cohomology.
Francesco Genovese: Deforming t-structures
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