Timeline for Is the completed tensor product (over a complete dvr) of two reduced complete Noetherian local rings again reduced?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 30 at 9:14 | answer | added | Satan's Minion | timeline score: 2 | |
| Jan 30 at 5:55 | comment | added | Satan's Minion | I think I can prove this, assuming A and B are O-flat. Will try to answer fully after the day's teaching... | |
| Jan 30 at 4:48 | comment | added | user521295 | @Z.M Thanks! I have edited the question to better align with its applications. | |
| Jan 30 at 4:40 | history | edited | user521295 | CC BY-SA 4.0 |
added assumptions to better align with its application
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| Jan 29 at 19:26 | comment | added | Z. M | I think that the counterexample in an answer to one of your linked questions gives rise to a counterexample, namely, let $\mathcal O=\mathbb Z_p$, $A=\mathbb Z_p[\![t]\!]/(t^2-p)$, and $B=\mathbb Z_p/p=\mathbb F_p$. Then the completed tensor product $A\hat\otimes_{\mathcal O}B=\mathbb F_p[\![t]\!]/(t^2)$ is non-reduced. The result might be true when $A$ and $B$ are $\mathcal O$-flat, but I do not come up with a proof. | |
| S Jan 29 at 15:31 | review | First questions | |||
| Jan 29 at 15:36 | |||||
| S Jan 29 at 15:31 | history | asked | user521295 | CC BY-SA 4.0 |