Timeline for Geometric interpretation of Iwasawa algebras: $\mathbb{Z}_p[[T]]$ as a disk?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2023 at 2:48 | vote | accept | Hetong Xu | ||
| May 27, 2023 at 15:14 | comment | added | David Loeffler | Yes, I meant the norm $\|f\|$ as defined in Alexey Do's answer (this is generally called the "Gauss norm"). | |
| May 27, 2023 at 1:52 | comment | added | Hetong Xu | Ah, I see! So here by saying norm, I guess you mean the norm of a function $f$ defined in Alexey Do's answer? Thank you! | |
| May 27, 2023 at 1:38 | comment | added | David Loeffler | (Important to note that $\mathbb{Z}_p[[T]] \otimes_{\mathbb{Z}_p} \mathbb{Q}_p$ is not the same as $\mathbb{Q}_p[[T]]$ -- the former is much smaller. If this isn't obvious to you, then you should reflect on the definitions a bit until it becomes so.) | |
| May 27, 2023 at 1:36 | comment | added | David Loeffler | $\Lambda = $ analytic functions on the unit disc whose norm is bounded by 1. On the other hand $\Lambda \otimes \mathbb{Q}_p$ = bounded analytic functions on the unit disc (but the bound can be anything). | |
| May 27, 2023 at 1:32 | comment | added | Hetong Xu | Thank you so much! Your answers have always been of great help! Still one more doubt that often comes to me: regarding elements in $\Lambda$ as functions from $\mathbb{C}_p$-disk to $\mathbb{C}_p$, then what is the corrrsponding interpretation after tensoring $\Lambda$ with $\mathbb{Q}_p$? Besides, I have always seen people tensoring $\Lambda$ with other things, for example $\mathcal{O}_L^{ur}$, or rational $\mathbb{Q}_p$, but sadly, I cannot feel the real difference after additional tensorings. | |
| May 26, 2023 at 5:20 | history | answered | David Loeffler | CC BY-SA 4.0 |