Timeline for How to picture $\mathbb{C}_p$?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2011 at 16:41 | comment | added | Alex B. | @Bo Peng: thanks, the pictures are certainly pretty. As I have indicated above, such pictures don't actually help me work with these objects, but they can definitely be fun. | |
| Feb 24, 2011 at 16:05 | comment | added | Bo Peng | about visualizing Q^{ab}... I think this page can help you a little bit : seesar.lbl.gov/anag/staff/ligocki/MathMusing/PolyRoots/… | |
| Jan 13, 2011 at 16:10 | vote | accept | Phillip Williams | ||
| Jan 13, 2011 at 8:35 | comment | added | Alex B. | That was the point of my last sentence in 2.: you can only view each term of the Cauchy sequence as a power series in its own uniformiser, but you cannot choose the same uniformiser for all the terms (so I personally don't regard that as a particularly helpful way of thinking about the elements of $\mathbb{C}_p$, I was just trying to offer something to the OP, since he was asking how he can think of them). | |
| Jan 13, 2011 at 8:34 | comment | added | Alex B. | Dear Martin, sorry if I was ambiguous. I was merely saying that each element of your Cauchy sequence lies in a finite extension. Of course, if all the elements lie in the same extension, then the limit of the sequence already exists in that extension (since it's complete) and you don't get anything new. The new elements of $\mathbb{C}_p$ can only be represented by Cauchy sequences in which the elements lie in infinitely many different extensions. | |
| Jan 13, 2011 at 8:19 | comment | added | Martin Brandenburg | I have a question to point 2. You seem to choose a finite extension of Q_p in which the whole sequence lies, right? But why does it exist? For me it's only obvious that we have a countable-generated algebraic extension. | |
| Jan 13, 2011 at 4:04 | history | answered | Alex B. | CC BY-SA 2.5 |