Quasi-coherent torsion sheaves, the semiderived category, and the semitensor product: Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes
arXiv:2104.05517 · doi:10.1007/978-3-031-37905-5
Abstract
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.
LaTeX 2e with xy-pic and mathrsfs.sty; 185 pages, 26 commutative diagrams; v.7: improvement in Lemma 5.2(c), Subsections 0.1-0.4 inserted in the Introduction, Appendix added; v.8: Remark 7.6 inserted; v.9: Subsection 11.4, discussing the loop group example, added; v.10: numbering of theorems in the Appendix corrected, no other changes -- the publisher's version is more complete