Timeline for Weierstrass subdomain of $\DeclareMathOperator\Spm{Spm}\Spm \mathbb{Q}_p$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2023 at 16:23 | comment | added | kindasorta | Thank you very much. Indeed I only proven that there is a map $\mathbb{Q}_p[[1/p]]\longrightarrow \mathbb{Q}_p\langle 1/p\rangle$, and didn't bother checking that it is injective/bijective because I thought it was obvious, however, indeed, there is an element $\infty = 1 + p\cdot \frac{1}{p} + p^2\cdot \frac{1}{p^2} + ...$ which lives in the target that doesn't live in the source, since it is the inverse of $0$, which is $1 - p\cdot \frac{1}{p}$, the target is indeed the 0 ring. Thank you so much! | |
| Feb 3, 2023 at 15:50 | comment | added | Jérôme Poineau | The problem is with your computation of $\mathbb{Q}_p\langle 1/p \rangle$. This is actually the ring $0$. It is obtained by moding out $\mathbb{Q}_p\langle X \rangle$ by the ideal generated by $X-1/p$, but the element $X-1/p = (1-pX)\times (-1/p)$ is invertible. | |
| Feb 3, 2023 at 15:14 | history | asked | kindasorta | CC BY-SA 4.0 |