JournalsprimsVol. 45 , No. 1DOI 10.2977/prims/1234361156

The Unipotent Albanese Map and Selmer Varieties for Curves

  • Minhyong Kim

    Korea Institute for Advanced Study (KIAS), Seoul, South Korea
The Unipotent Albanese Map and Selmer Varieties for Curves cover

Abstract

We study the unipotent Albanese map that associates the torsor of paths for p-adic fundamental groups to a point on a hyperbolic curve. It is shown that the map is very transcendental in nature, while standard conjectures about the structure of mixed motives provide control over the image of the map. As a consequence, conjectures of ‘Birch and Swinnerton-Dyer type’ are connected to finiteness theorems of Faltings–Siegel type.