# projective dimension of finitely generated modules over char 0

In the paper "On modules of finite projective dimension over complete intersection" Dutta proved that a finitely generated module over a local complete intersection ring over char $p>0$ has finite projective dimension if it satisfies certain condition on Tor. I am wondering if there are any similar results over char $0$. I am mainly interested in finitely generated module over homogeneous coordinate rings of projective varieties.

• One may hope to obtain a similar result in characteristic $0$ if the ring has a contracting endomorphism whose closed fiber is of finite length. However, this is not an easy question and the proofs in the case of Frobenius from the paper that you cited do not immediately generalize to arbitrary endomorphisms. – Mahdi Majidi-Zolbanin May 29 '12 at 18:04