On $abc$ and discriminants

Abstract

We modify the $abc$-conjecture for number fields $K$ in order to make the support (like the height) well-behaved under field extensions. We show further that the exponent $\mu >1$ of the absolute value $D_K$ of the discriminant cannot be replaced by $\mu =1$, and even that an arbitrarily large power of $\log D_K$ must be present.

Locations

• Proceedings of the American Mathematical Society - View - PDF