L. A. Betts

collaborators

3 papers

math.NT2026

Chabauty--Kim, finite descent, and the Section Conjecture for locally geometric sections

L. Alexander Betts, Theresa Kumpitsch, Martin LÃ¼dtke

Let $X$ be a smooth projective curve of genus $\geq 2$ over a number field. A natural variant of Grothendieck's Section Conjecture postulates that every section of the fundamental e…

math.AG2025

A motivic Weil height machine for curves

L. Alexander Betts, Ishai Dan-Cohen

The rational points of a smooth curve $X$ over a number field $k$ map to the set of augmentations of the associated motivic algebra. An expectation, related to Kim's conjecture, is…

math.NT2025

Rational points on the non-split Cartan modular curve of level 27 and quadratic Chabauty over number fields

Jennifer S. Balakrishnan, L. Alexander Betts, Daniel Rayor Hast +2

Thanks to work of Rouse, Sutherland, and Zureick-Brown, it is known exactly which subgroups of GL $_{2} (Z_{3})$ can occur as the image of the $3$ -adic Galois representation att…