Let $(A,m,k)$ be commutative noetherian local ring.
Can one detect if $A$ is a Gorenstein ring from the André–Quillen homologies $H_n(A,k,-)$?
Let $(A,m,k)$ be commutative noetherian local ring.
Can one detect if $A$ is a Gorenstein ring from the André–Quillen homologies $H_n(A,k,-)$?
"No" if you want a standard vanishing result, and "no up to now" if you are thinking in another kind of characterization (see however for a related result: Garcia-Soto, Ascent and descent of Gorenstein property, Glasgow Math. J. 46 (2004) 205–210).