$(R,m)$ is a local Noetherian ring. $M$ is a finite $R$-module.

Here, using dualizing complex, *Karl Schwede* says that if $R=S/I$ where $S$ is regular of dimension $d$, then we have: "**$H^i_m(M)$ is finitely generated** iff **the support of $Ext^{d-i}_S(M, S)$ has dimension zero**".

Question:can one prove this,Not using dualizing complex

thank you