This talk is based on the book Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes—quasi-coherent torsion sheaves, the semiderived category, and the semitensor product. I will start with some examples serving as special cases of the general theory, such as the tensor structure on the category of unbounded complexes of injective quasi-coherent sheaves on a Noetherian scheme with a dualizing complex. Then I will proceed to explain the setting of a flat affine morphism of ind-schemes into an ind-Noetherian ind-scheme with a dualizing complex, and the main ingredient concepts of quasi-coherent torsion sheaves, pro-quasi-coherent pro-sheaves, and the semiderived category. In the end, I will spell out the construction of the semi-tensor product operation on the semi-derived category of quasi-coherent torsion sheaves, making it a tensor triangulated category.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
