Let V be a fixed algebraic variety defined by m polynomials in n variables with integer coefficients. We show that there exists a constant C(V) such that for almost all primes p for all but at most C(V) points on the reduction of V modulo p at least one of the components has a large multiplicative order. This generalises several previous results and is a step towards a conjecture of B. Poonen.
|Number of pages||15|
|Journal||Journal de Theorie des Nombres de Bordeaux|
|Publication status||Published - 2014|