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Accepted

• 102k
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 ...
• 20k

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 ...
• 5,890
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'...
• 176k

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.

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 ...
• 9,993