Timeline for How to compute the integer corresponding to a class in $G_0(B_{\mathrm{red}})$ for a commutative noetherian ring $B$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2023 at 1:11 | comment | added | Boris | @Vik78 Thank you very much for providing this detailed reference. This is very kind of you. | |
| Jul 7, 2023 at 23:21 | comment | added | Vik78 | @Boris math.wustl.edu/~kumar/papers/seshadri.pdf i have a feeling the intended result is here | |
| Feb 8, 2023 at 12:40 | comment | added | Boris | Hello Mohan. I have trouble showing that $P$ is a free $A$-module. By the Auslander-Buchsbaum formula, I need to show that the depth of $P$ equals the depth of $A$. But I don’t know how to check this. And for the Seshadri’s theorem you mentioned, what I found on Google is a theorem about holomorphic vector bundles on Riemann surfaces. Could you please help me with these issues? Thank you so much. | |
| Feb 7, 2023 at 23:31 | comment | added | Boris | Hello Mohan, thank you so much for your kind help. I understand that $R$ is an $A$-algebra of finite type now. I just found the statement of the Auslander-Buchsbaum formula. Hopefully I will figure out how this formula implies that $P$ is a free $A$-module. | |
| Feb 7, 2023 at 22:24 | comment | added | Mohan | @Boris $R$ is clearly finite type, since it is generated by $xy, xy^2,\ldots, xy^{m-1}$ over $A$. For the second comment, I quoted two non- trivial theorems, though you can get away with Auslander- Buchsbaum. | |
| Feb 7, 2023 at 22:08 | comment | added | Boris | 2. Assuming that you set P to be the kernel of the surjective A-module homomorphism $F\rightarrow M$, then how do you show that P is free? Thank you so much for your kind help. | |
| Feb 7, 2023 at 22:06 | comment | added | Boris | 1. How do you show that R is a finitely generated A-module? I understand that R is an integral A-algebra. But if I am not mistaken, we also need R to be a finite-type A-algebra, which I don’t know how to check in this case. | |
| Feb 7, 2023 at 22:04 | comment | added | Boris | Hello Mohan, thank you so much for kindly providing these detailed explanations of your answer. I am stuck on some parts of your proof. | |
| Feb 7, 2023 at 21:04 | history | edited | Mohan | CC BY-SA 4.0 |
added 5 characters in body
|
| Feb 7, 2023 at 20:35 | history | answered | Mohan | CC BY-SA 4.0 |