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arXiv · 1606.09618

Diophantine and tropical geometry, and uniformity of rational points on curves

Eric Katz·Joseph Rabinoff·David Zureick-Brown
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Abstract

We describe recent work connecting combinatorics and tropical/non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curves and for torsion packets of curves. The method of Chabauty--Coleman lies at the heart of this connection, and we emphasize the clarification that tropical geometry affords throughout the theory of $p$-adic integration, especially to the comparison of analytic continuations of $p$-adic integrals and to the analysis of zeros of integrals on domains admitting monodromy.

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Eric Katz, Joseph Rabinoff, David Zureick-Brown. 2016-06-30. Diophantine and tropical geometry, and uniformity of rational points on curves. https://arxiv.org/abs/1606.09618

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