L. A. Betts

activity

20182022

most citedWeight filtrations on Selmer schemes and the effective Chabauty--Kim method

1 citations · 2 across the 2 of their papers we have counts for

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6 papers · 1 filter

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…

math.NT2022★ 1 cited

Galois sections and $p$ -adic period mappings

L. Alexander Betts, Jakob Stix

Let $K$ be a number field not containing a CM subfield. For any smooth projective curve $Y / K$ of genus $\geq 2$ , we prove that the image of the "Selmer" part of Grothendieck's secti…

math.NT2021★ 1 cited

Weight filtrations on Selmer schemes and the effective Chabauty--Kim method

L. Alexander Betts

We develop an effective version of the Chabauty--Kim method which gives explicit upper bounds on the number of $S$ -integral points on a hyperbolic curve in terms of dimensions of c…

math.NT2019

Semisimplicity and weight-monodromy for fundamental groups

L. Alexander Betts, Daniel Litt

Let X be a smooth, geometrically connected variety over a p-adic local field. We show that the pro-unipotent fundamental group of X (in both the etale and crystalline settings) sat…

math.NT2019

The local theory of unipotent Kummer maps and refined Selmer schemes

L. Alexander Betts, Netan Dogra

We study the Galois action on paths in the $Q_{ℓ}$ -pro-unipotent étale fundamental groupoid of a hyperbolic curve $X$ over a $p$ -adic field with $ℓ \neq = p$ . We prove an…

math.NT2018

Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction