Name: Srikanth Iyengar
Title: Andr\'e-Quillen homology of algebra retracts
Abstract:
Let $\varphi\colon R\to S$ be a homomorphism of commutative, noetherian rings.
This talk will be concerned with the Andr\'e-Quillen homology $\mbox{D}_n(S|R,M)$
of the $R$-algebra $S$ with coefficients in an $S$-module $M$. A major focus of
research in this subject has been the relationship between the vanishing of
$\mbox{D}_n(S|R,-)$ and the structural properties of the ring homomorphism $\varphi$.
In this context, Quillen has posed the
{\em Conjecture.} If $\mbox{D}_n(S|R,-)$ for $n\gg 0$, then $\mbox{D}_n(S|R,-)$ for
$n\ge 3$.
Recently, Avramov and I have settled this in the affirmative in the case where $\varphi$
admits a splitting: A homomorphism $\psi\colon S\to R$ such that $\varphi\circ\psi=1^S$.
I propose to give an brief survey of the various results that have been established
on the vanishing of the Andr\'e-Quillen homology, leading up to my work with Avramov.