Let R be a local ring. Let J ⊂ R be an ideal generated by a Koszul-regular sequence. Let I ⊂ J be an ideal such that R/I is a perfect object of D(R) and such that R/J is a perfect object of D(R/I). Then, is it true that I and J/I are generated by Koszul-regular sequences in R and R/I?
In the Noetherian case you can just say “regular sequence” and the conditions just mean that I has finite projective dimension over R and R/J has finite projective dimension over R/I. But the way the question is formulated makes it believe-able that if the question has answer “yes” in the Noetherian case then the answer is yes in the general case. I have tried to prove this and I have tried to find counter examples, but I failed on both counts. I would appreciate any comments or suggestions.