Minhyong Kim

The motivic fundamental group of P1∖{0,1,∞} and the theorem of Siegel

In this paper, we establish a link between the structure theory of the pro-unipotent motivic fundamental group of the projective line minus three points and Diophantine geometry. In particular, we give a p-adic proof of Siegels theorem.

Massey products for elliptic curves of rank 1

For an elliptic curve over Q of analytic rank 1, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p-adic points.

Selmer varieties for curves with CM Jacobians

We study the Selmer variety associated to a canonical quotient of the

A De Rham-Witt approach to crystalline rational homotopy theory

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Appendix and erratum to “Massey products for elliptic curves of rank 1”

-pro-unipotent fundamental group of a smooth projective curve of genus at least two defined over

Geometric height inequalities and the Kodaira-Spencer map

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A

whose Jacobian decomposes into a product of abelian varieties with complex multiplication. Elementary multi-variable Iwasawa theory is used to prove dimension bounds, which, in turn, lead to a new proof of Diophantine finiteness over

p

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-adic nonabelian criterion for good reduction of curves

for such curves.

Diophantine Geometry and Non-abelian Reciprocity Laws I

We give a definition of the crystalline fundamental group of suitable log schemes in positive characteristic using the techniques of rational homotopy theory applied to the DeRham-Witt complex. 1 2