2-Adic point counting on K3 surfaces

This article reports on an approach to point counting on algebraic varieties over finite fields that is based on a detailed investigation of the 2-adic orthogonal group. Combining the new approach with a p-adic method, we count the number of points on some K3 surfaces over the field Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{\!p}$$\end{document}, for all primes p<108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p < 10^8$$\end{document}.