Abstract
We study the behavior of geometric Picard ranks of K3 surfaces over under reduction modulo primes. We compute these ranks for reductions of smooth quartic surfaces modulo all primes p < 216 in several representative examples and investigate the resulting statistics.
2000 AMS Subject Classification::
Notes
1FLINT, written by William Hart, Fredrik Johansson, and Sebastian Pancratz, is available at http://flintlib.org. NTL, by Victor Shoup, is available at http://www.shoup.net/ntl/. The raw data of all experiments are available at www.cims.nyu.edu/~costa.