# Tag Info

Accepted

Accepted

### Why is the section conjecture important?

You can start here "Fermat's last theorem" and anabelian geometry?? In particular, I mention there that: At some point Deligne thought he had a proof that the section conjecture implied ...
Accepted

### History of the connection between Riemann surfaces and complex algebraic curves

The connection came from the paper by Dedekind and Weber "Theorie der algebraischen Functionen einer Veranderlichen", Crelle's Journal, 1882. In this paper the authors recover the theory by Riemann (...
Accepted

### Are there integer solutions to $3y^2 = 4x^3-1$ other than $(1,1)$ and $(1,-1)$?

The projective form of your curve is $3y^{2} z = 4x^{3} - z^{3}$. This has three obvious points: $(1 : 1 : 1)$, $(1 : -1 : 1)$, and $(0 : 1 : 0)$. Your curve is isomorphic over $\mathbb{Q}$ to the ...
Accepted

### History of Study's Lemma?

I found the lemma on page 63 of Study's Einleitung in die Theorie der Invarianten linearer Transformationen auf Grund der Vektorenrechnung (1923). The source cited for the proof is page 202 of Study'...

### History of the connection between Riemann surfaces and complex algebraic curves

I have always felt this was due to Riemann himself: especially in: Theory of Abelian Functions, 1857. Of course the association of a Riemann surface to an algebraic curve is generally attributed to ...

### Automorphisms of cartesian products of curves

That is certainly not true. Consider the case that $C$ is an elliptic curve. Then $\text{Aut}(C\times C)$ contains $\text{GL}(2,\mathbb{Z})$ as a subgroup.

### Motivations to study the cohomology of the moduli space of curves

As the title to Mumford's famous paper "Toward an enumerative geometry..." suggests, knowing the cohomology / cycle theory of the moduli space of curves allows one to answer enumerative geometry ...

### Is Proposition 2.6 in J. Silverman's book Arithmetic of Elliptic Curves correct?

The reason is that there are two ways of thinking about "points". Let $A$ be a ring. Then, define: A scheme-theoretic/topological point of Spec $A$ is a prime ideal of $A$. A geometric/functorial ...