Speaker: Ben Briggs
Title: Homological characterisations of complete intersections, borrowing from rational homotopy theory
Abstract: For an ideal I of finite projective dimension in a local ring R, Quillen conjectured that I is complete intersection if and only if the cotangent complex of R/I over R has finite projective dimension. This was established by Avramov in 1999; in topology it corresponds to the characterisation of elliptic spaces in terms of the rational homotopy Lie algebra. Vasconcelos made a similar conjecture: I is complete intersection if and only if the conormal module I/I^2 has finite projective dimension over R/I. I will try to explain how one can prove these two conjectures together, emphasising the parallels with rational homotopy theory (and I’ll try to explain all the needed background). This is joint work with Srikanth Iyengar.