APS
Speaker: Aditya Dwivedi, IIT Bombay
Host: Manoj K Keshari
Title: A cotriple perspective on the HKR theorem
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, September 28
Venue: Room 113
Abstract: The Hochschild-Kostant-Rosenberg (HKR) theorem states that for a smooth commutative algebra A over a field k, the Hochschild homology of A is isomorphic to the exterior powers of the module of Kahler differentials:
HHn(A,A) \iso \omega^n A/k.
In this talk I will present a cotriple perspective on this result. The free-forgetful adjunction between commutative k-algebras and k-modules gives rise to a cotriple resolution of A by polynomial algebras, and applying the Hochschild complex levelwise produces a first-quadrant spectral sequence converging to HH*(A,A). Its E2-page is given by the homology of the exterior powers of the cotangent complex, so the HKR isomorphism is equivalent to the vanishing of the higher Andre-Quillen homology of A.This forces the spectral sequence to collapse at E2, recovering the HKR isomorphism and making explicit the role of smoothness in the proof.