Suppose we have a small category $\mathcal{I}$, a diagram $D : \mathcal{I} \to \mathcal{C}$, and a functor $F : \mathcal{C} \to \mathcal{D}$. De know that the functor $\hat{F} : \text{Cone}_{\mathcal{C}}(D) \to \text{Cone}_\mathcal{D}(F \circ D)$ preserves the terminal object(s). In categories wi...
$e^{1/z}$ has an essential singularity at $z=0$, which by the Casorati–Weierstrass theorem implies that for every complex number $W$ there is a sequence $z_k\to 0$ with $e^{1/z_k}\to W$.
Is there some elegant way to see this directly without proving Casorati–Weierstrass first? (I know that the pr...
Let $E$ be an elliptic curve $X^3+Y^3+60Z^3=0$ and $C$ be a genus $1$ curve given by $C:3X^3+4Y^3+5Z^3=0$.
I want to prove elliptic curve $E$ is Jacobi variety of $C$.
What I should to prove is that $Pic^0(C) \cong E$ as a group.
But I cannot come up with explicit isomorphism.
Cassel's lecture...
tentatively, i think we can probably go ahead with it. I've gone back in the logs and reviewed the prior objections from within the mod team, and it seems like only one had objections and they are no longer active, so between that and the votes on meta I think we can call it a consensus
so: the plan would be grad-div-curl, curl and gradient would be synonyms (not divergence, we are going to kill that tag whenever it gets created due to ambiguity with divergence in the sense of convergence-divergence)
Let $E$ be an elliptic curve $X^3+Y^3+60Z^3=0$ and $C$ be a genus $1$ curve given by $C:3X^3+4Y^3+5Z^3=0$.
I want to prove elliptic curve $E$ is Jacobi variety of $C$.
What I should to prove is that $Pic^0(C) \cong E$ as a group.
But I cannot come up with explicit isomorphism.
Cassel's lecture...
