Quasi-coherent torsion sheaves, the semiderived category, and the semitensor product: Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes

We construct the semi-infinite tensor structure on the semiderived category of quasi-coherent torsion sheaves on an ind-scheme endowed with a flat affine morphism into an ind-Noetherian ind-scheme with a dualizing complex. The semitensor product is “a mixture of” the cotensor product along the base and the derived tensor product along the fibers. The inverse image of the dualizing complex is the unit object. This construction is a partial realization of the Semi-infinite Algebraic Geometry program, as outlined in the introduction to arXiv:1504.00700.