2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103748We discuss $p$-adic unipotent Albanese maps for curves of positive genus, extending the theory of $p$-adic multiple polylogarithms. This construction is then used to relate linear Diophantine conjectures of `Birch and Swinnerton-Dyer type' to non-linear theorems of Faltings-Siegel type.One minor error and several misprints correctedNumber TheoryAlgebraic Geometry14G05;11G30;11G55text