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Feb
8
comment Fixed fields in Neukirch's book (chap. IV): notational problem
My guess would be: $\tilde \sigma$ generates a cyclic subgroup of the profinite (and possibly finite) group $G_K/G_{\tilde L}$; take the closure of this subgroup in $G_K/G_{\tilde L}$; look at its canonical preimage inside $G_K\subset G$; this is the closed subgroup of $G$ corresponding to the desired "fixed field"...
Feb
8
revised Does Magma let you specify primary invariants?
added 14 characters in body
Feb
7
revised Probability theory with the hyperreals?
added 158 characters in body
Feb
7
accepted Probability theory with the hyperreals?
Feb
7
asked Probability theory with the hyperreals?
Feb
7
comment Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
+1 I look forward to reading this over.
Feb
5
revised Does Magma let you specify primary invariants?
at suggestion of a bot, adding a broader tag
Feb
5
asked Does Magma let you specify primary invariants?
Feb
4
comment Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
@Lubin - Thank you, yes I know that theorem. What I was unsure about is the relationship of $N(a)$ to $[R_\mathfrak{P}:a R_\mathfrak{P}]$. How does one prove that the $p$-valuation of $[R_\mathfrak{P}:aR_\mathfrak{P}]$ is related to the norm of $a$ in this way? Is your point that the $p$-valuation of $[R_\mathfrak{P}:aR_\mathfrak{P}]$ is the same as the $\mathfrak{P}$-valuation of $a$? (Since $aR_\mathfrak{P} = \pi^{v_\mathfrak{P}}R_\mathfrak{P}$ for $\pi$ a uniformizer for the DVR $R_\mathfrak{P}$?)
Feb
3
comment Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
(1) Is it true that for $R_\mathfrak{P}$ the $p$-valuation of $[R_\mathfrak{P}:\alpha R_\mathfrak{P}]$ is given by that of $\mathbf{N}(\alpha)$? (Certainly there is no hope that these numbers will match beyond their $p$-valuations.) What's the argument? and (2) ... hmmm I thought I had another question but I guess (1) was really the only uncertainty left.
Feb
3
comment Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
@Lubin - that sounds like the right idea to me - I don't believe the result should depend on class number issues. I'm missing a couple steps though. I guess the idea is that one captures the $p$-valuation of $[R^n:MR^n]$ (letting $R=\mathcal{O}_K$ and observing that $\Lambda = MR^n$) by taking a $\mathfrak{P}\mid p$ and then taking the $p$-valuation of $[R_\mathfrak{P}^n:MR_\mathfrak{P}^n]$, and then combining over all $p$ for which the valuation is positive. (Since $R_\mathfrak{P}$ is a PID, Mariano's SNF argument applies for each $\mathfrak{P}$.) I have 2 questions to finish this:
Feb
3
revised Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
added 2 characters in body
Feb
3
revised Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
added 185 characters in body
Feb
3
comment Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
@MarianoSuárez-Alvarez - but it will work over fields of class number 1?
Feb
2
revised Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
added 447 characters in body
Feb
2
asked Does the determinant give you the index over $\mathcal{O}_k$ as well as over $\mathbb{Z}$?
Jan
23
comment A function that is $L^p$ for all $p$ but is not $L^\infty$?
+1 but note that morally this is the same example as Jonas' - observe that your $f$ is bounded by constant multiples of $-\log x$.
Jan
12
answered Is the answer of $\ \ 2415^n \ mod \ \ 2556 \ \ $ is only $711$ and $1989$ for $n\in \mathbb{Z}^{+} >1 \ \ ?$
Jan
10
awarded  Enlightened
Jan
10
awarded  Nice Answer