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?<\/p>\n
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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 … Continue reading