2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69845We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several strands to discuss a possible approach to establishing a cohomological interpretation of the complex dimensions.To appear in Proceedings of Symposia of Pure Mathematics, title: "Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot"Number TheoryPrimary 11M41, 28A80; Secondary 11G20, 11J70text