We use motivic fundamental groups to show that -integral points on a unirational variety over a totally real number field whose fundamental group is nonabelian enough in a certain sense can be covered by zero loci of finitely many nonzero -adic analytic functions. In particular, in the -dimensional case we obtain a motivic proof of finiteness of -integral points of punctured projective line over totally real number fields, which gives as a special case a motivic proof of Siegel’s theorem over and totally real quadratic number fields.
Majid Hadian. "Motivic fundamental groups and integral points." Duke Math. J. 160 (3) 503 - 565, 1 December 2011. https://doi.org/10.1215/00127094-1444296