All Questions

Is there a general algorithm that can compute in finite time all rational points on any curve of genus $g\geq 2$ whose Jacobian has rank $0$? If not, for what special cases such algorithm is known? ...

There are facts in Mathematics that are so "obvious" and "well-known" that no-one includes a proper proof. An example is: Theorem: If polynomial $P(x,y)$ with rational coefficients ...

We found infinitely many integer solutions to $$X^4+Y^4-18Z^4= -16 \qquad (1)$$. The interesting part in this diophantine equation is the sum of the reciprocals of the degrees is $3/4 < 1$, which ...

I am interested in papers that investigates the existence or non-existence of curves of low degree (relative to the degree of the ambient variety). The starting example is that of surfaces and ...