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Feb
6
answered How would I translate this sentence into a predicate formula
Feb
5
awarded  Yearling
Feb
3
comment Affine variety of geometric progressions.
Again, if $a_2=0$ and $a_3=0$ then the equation $a_1 a_4 = a_2 a_3$, which results from $\frac{a_2}{a_1} = \frac{a_4}{a_3}$, says that either $a_1$ or $a_4$ is zero. Since you require $a_1\neq 0$, it will force $a_4$ to be zero as well.
Feb
2
comment Affine variety of geometric progressions.
In fact, it does not. The equation $a_1 a_3 = a_2^2$, which results from $\frac{a_2}{a_1}=\frac{a_3}{a_2}$, is not satisfied by points with $a_3=a_4=0$ and $a_2\neq 0$.
Feb
1
answered Affine variety of geometric progressions.
Feb
1
awarded  Scholar
Feb
1
accepted Local reciprocity map applied to norm
Feb
1
comment Local reciprocity map applied to norm
Thanks for your help, @nguyen-quang-do . Re your first reply, I think it is the other composition, $N_{L/K}\circ i_{L/K}$, that is the $n$-th power map. Your second reply may be useful; I will do some looking for explicit reciprocity laws for my setup.
Jan
29
comment What are exact sequences, metaphysically speaking?
@leewangzhong 's exact sequences are good examples of trivial vs. nontrivial SES. So are direct vs. semidirect products. But the second example (with $\mathbb Z_4$ in the middle) is not a semidirect product because it does not have a section. Just wanted to clarify.
Jan
29
comment Local reciprocity map applied to norm
I guess for correctness I should insert $i_{L/K}$, but the $N_{L/K}$ is not an error. So to be precise, I'm asking about the composition $r_L\circ i_{L/K}\circ N_{L/K}$, or, in words, I want to know what is the result of applying $r_L$ to a norm. Taking your remark into consideration, a related question is, what can be said about applying the map $V$ to an element of $\text{Gal}(K^\text{ab}/L)$?
Jan
14
awarded  Autobiographer
Jan
12
answered Sheafyness and relative chinese remainder theorem
Jan
11
comment $\forall \varepsilon \in \mathbb{R}_{>0} \exists v \in V$ so that $x - \varepsilon < v$ if and only if $x = \sup V$
Your statement is incomplete. The $\forall\epsilon\dots$ is also true for any $x\in V$. You should add the condition that $x$ is an upper bound for the elements of $V$.
Jan
11
answered Isomorphism as $R$-module
Jan
11
revised Local reciprocity map applied to norm
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Jan
11
asked Local reciprocity map applied to norm
Jan
11
answered Neukirch and a congruence condition.
Jun
23
comment Galois action on torsion points of formal group
@Lubin, just found your comment and looked up Tate's and your paper; I believe you are referring to the Annals paper from 1965. It is indeed very clear and is likely the model for Neukirch's treatment. I appreciate the reference.
Jun
15
comment Galois action on torsion points of formal group
Thank you, @Lubin. That seems to be the case. I've also found a (in my opinion) clearer presentation in Neukirch's Algebraic Number Theory.
Jun
12
awarded  Student