Resumen de The number of extensions of a number field with fixed degree and bounded discriminant

Akshay Venkatesh, Jordan S. Ellenberg

• We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant ¡Ü X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.