2 problems

Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be $K$-algebras essentially of finite type over $K$. Assume that $B$ is a finite-dimensional pr…

Let $(A,m)$ be an Artinian local ring, and let $x_1,\ldots,x_n\in m$. Write $H_1(x_1,\ldots,x_n;A)$ for the first Koszul homology module of the sequence on $A$. Artinian Koszul hom…