The unipotent Albanese map and Selmer varieties for curves

Abstract

We 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 corrected

References in corpus (1)

• p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation