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math.AG2025
A motivic Weil height machine for curves
L. Alexander Betts, Ishai Dan-Cohen
The rational points of a smooth curve over a number field 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 can occur as the image of the -adic Galois representation att…