12 citations · 19 across the 13 of their papers we have counts for
13 papers
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…
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…
Chabauty--Kim, finite descent, and the Section Conjecture for locally geometric sections
L. Alexander Betts, Theresa Kumpitsch, Martin Lüdtke
Let be a smooth projective curve of genus over a number field. A natural variant of Grothendieck's Section Conjecture postulates that every section of the fundamental e…
Bounds on the Chabauty--Kim Locus of Hyperbolic Curves
L. Alexander Betts, David Corwin, Marius Leonhardt
Conditionally on the Tate--Shafarevich and Bloch--Kato Conjectures, we give an explicit upper bound on the size of the -adic Chabauty--Kim locus, and hence on the number of rati…
Galois sections and -adic period mappings
L. Alexander Betts, Jakob Stix
Let be a number field not containing a CM subfield. For any smooth projective curve of genus , we prove that the image of the "Selmer" part of Grothendieck's secti…
Local constancy of pro-unipotent Kummer maps
L. Alexander Betts
It is a theorem of Kim-Tamagawa that the -pro-unipotent Kummer map associated to a smooth projective curve over a finite extension of is locally c…
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 -integral points on a hyperbolic curve in terms of dimensions of c…
Refined Selmer equations for the thrice-punctured line in depth two
Alex J. Best, L. Alexander Betts, Theresa Kumpitsch +5
In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many -integral points on . One advantage of Kim…
A user's guide to the local arithmetic of hyperelliptic curves
Alex J. Best, L. Alexander Betts, Matthew Bisatt +8
A new approach has been recently developed to study the arithmetic of hyperelliptic curves over local fields of odd residue characteristic via combinatorial data associa…
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…
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 -pro-unipotent étale fundamental groupoid of a hyperbolic curve over a -adic field with . We prove an…
Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
L. Alexander Betts
We study how Tamagawa numbers of Jacobians of hyperelliptic curves vary as one varies the base field or the curve, in the case of semistable reduction. We find that there are stron…
Finite quotients of Z[C_n]-lattices and Tamagawa numbers of semistable abelian varieties
L. Alexander Betts, Vladimir Dokchitser
We investigate the behaviour of Tamagawa numbers of semistable principally polarised abelian varieties in extensions of local fields. In view of the Raynaud parametrisation, this t…