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The unipotent Albanese map and Selmer varieties for curves

Minhyong Kim
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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.

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Minhyong Kim. 2006-09-28. The unipotent Albanese map and Selmer varieties for curves. https://arxiv.org/abs/math/0510441

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