Gorensteinness of short local rings in terms of the vanishing of Ext and Tor

Dipankar Ghosh

Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring which contains a regular sequence $\underline{x}=x_1,\dots ,x_d\in \mathfrak{m}\setminus {\mathfrak{m}}^2$ su…