Kumar Murty

It is possible for a simple Abelian variety to factor mod p for every prime p. This is similar to the phenomenon of the irreducible pol-ynomial over the integers becoming reducible when reduced modulo any prime. We study this problem, especially its...

The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian...

The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian...