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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 Add more tags 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