2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157238The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative arithmetic surfaces and we prove an arithmetic Riemann-Roch theorem in this setup.20 pagesNumber TheoryAlgebraic Geometry14G40 (Primary), 14A22 (Secondary)text