The unipotent Albanese map and Selmer varieties for curves
نویسنده
چکیده
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. In a letter to Faltings [14] dated June, 1983, Grothendieck proposed several striking conjectural connections between the arithmetic geometry of ‘anabelian schemes’ and their fundamental groups, among which one finds issues of considerable interest to classical Diophantine geometers. Here we will trouble the reader with a careful formulation of just one of them. Let F be a number field and
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