Timeline for Restricted Iwasawa theory
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2018 at 16:06 | comment | added | Chris Wuthrich | mathoverflow.net/questions/182662/… could be relevant if you need one with $\mu>0$ | |
| Apr 30, 2018 at 16:01 | comment | added | Chris Wuthrich | yes ............ | |
| Apr 30, 2018 at 14:59 | comment | added | Pablo | @ChrisWuthrich this is indeed a necessary condition but, perhaps due to my ignorance, I do not see why it is sufficient. Is it explained in Washington’s book? | |
| Apr 30, 2018 at 14:48 | comment | added | Chris Wuthrich | Isn't it just $\mu\cdot n + \mathbf{O}(1)$ ? If so you need to stay away from the cyclotomic one as we expect $\mu=0$ there. | |
| Apr 30, 2018 at 9:21 | comment | added | Pablo | @ChrisWuthrich Thanks! Is there an example where the $p$-rank of the class group of $K_n$ grows as a linear function of $[K_n : K]$ ? | |
| Apr 30, 2018 at 9:17 | comment | added | Chris Wuthrich | For instance: The $p$-rank of the class group of $K_n$ is bounded if and only if $\mu=0$ (Washington Prop 13.23). In that chapter, you will find the tools to answer the second question. | |
| Apr 29, 2018 at 20:33 | comment | added | Pablo | @ChrisWuthrich, you are right, but can you please elaborate? | |
| Apr 29, 2018 at 20:31 | comment | added | Chris Wuthrich | $X_0$ is $X/pX$. Iwasawa's theorem on the growth of the $p$-primary part of the class group tells you more than the size, it also tells us about its structure. | |
| Apr 29, 2018 at 16:56 | history | asked | Pablo | CC BY-SA 3.0 |