Timeline for Categorical description of the restricted product (Adeles)
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 10, 2012 at 8:20 | comment | added | Marc Palm | Isn't the fact that your construction is the same is called strong approximation. The ring $\mathbb{Q} \otimes_{\mathbb{Z}} \widehat{\mathbb{Z}}$ seems not so explicit to my taste, but nice picture. | |
| May 10, 2012 at 0:08 | comment | added | paul garrett | In the spirit of the situation, rather than literally saying that the opens are $q\times \hat{\mathbb Z}$, perhaps saying to give $\mathbb Q$ the discrete topology would be nicer, and then "tensor product" as linearizing bilinear maps, etc. Similarly, stylistically, if we've talked about topologies on tensor products for that reason, then we can avoid talking about choosing bases for $K$, etc. Just quibbles... :) | |
| May 9, 2012 at 21:26 | comment | added | Neil Strickland | @Konrad: I edited the answer to include some comments about topologies. | |
| May 9, 2012 at 21:25 | history | edited | Neil Strickland | CC BY-SA 3.0 |
Added comments about topologies
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| May 9, 2012 at 21:06 | comment | added | Konrad Voelkel | Thanks. To make that description work for me, there must be a natural topology on the tensor product of topological rings. What is it? | |
| May 9, 2012 at 18:02 | history | answered | Neil Strickland | CC BY-SA 3.0 |