Back to Commutative Algebra Seminar: Fall 2017
Commutative Algebra Seminar
Date: Friday, Nov 3, 2017
Time: 2:30PM - 3:20PM
Location: LCB 215
Benjamin Briggs
University of Toronto
Title |
Long exact sequences for the homotopy Lie algebra and the L.S. category of a homomorphism |
Abstract |
The minimal model of a local map $\phi: R\ to S$ presents a graded Lie algebra $\pi^(\phi)$, known as the homotopy Lie algebra of $\phi$. While $\pi^(\phi)$ produces sensible results from the perspective of Koszul duality, it has poor formal properties. In particular, one would like a long exact sequence of homotopy Lie algebras from a fibre sequence, analogous to the topological situation. Andr'e-Quillen cohomology repairs these formal defects, but produces strange results from the the Koszul duality perspective. I will present a variation on $\pi^$, namely $\lambda^$, which enjoys many of the formal properties of Andr'e-Quillen cohomology while also producing the expected Koszul Duality results. In particular, $\lambda^$ possesses a Jacobi-Zariski long exact sequence in all situations, and vanishing of $\lambda^$ characterises regular, complete intersection, and quasi-complete intersection homomorphisms. |
Commutative Algebra