Diophantine and tropical geometry, and uniformity of rational points on curves
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2016
- DOI:
- 10.48550/arXiv.1606.09618
- arXiv:
- arXiv:1606.09618
- Bibcode:
- 2016arXiv160609618K
- Keywords:
-
- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry;
- 14G05 (Primary) 11G20;
- 11G30;
- 14G22;
- 14H25;
- 14K20;
- 14T05 (Secondary)
- E-Print:
- 49 pages, 7 figures, minor revisions