Alexander Betts
Postdoctoral Researcher in Mathematics
(Image credit: Kush Singhal)
Contact details
Postal address:
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138
Email:
abetts[at]math[dot]harvard[dot]edu
Publications and preprints
Publications
- Refined Selmer equations for the thrice-punctured line in depth two (with A.J. Best, T. Kumpitsch, M. Lüdtke, A.W. McAndrew, L. Qian, E. Studnia and Y. Xu) Math. Comp., to appear arXiv:2106.10145
- Local constancy of pro-unipotent Kummer maps Proc. Lond. Math. Soc., 127(3), pp836–888, 2023 doi:10.1112/plms.12554 | arXiv:2203.03701 | Erratum
- Weight filtrations on Selmer schemes and the effective Chabauty–Kim method Compos. Math., 159(7) pp1531–1605, 2023 doi:10.1112/S0010437X2300725X | arXiv:2106.01218
- The motivic anabelian geometry of local heights on abelian varieties Mem. Amer. Math. Soc., to appear arXiv:1706.04850
- Semisimplicity of the Frobenius action on π1 (with D. Litt) in Proceedings of the Simons Symposium on p-adic Hodge Theory, Singular Varieties and Non-Abelian Aspects, pp17–64, 2023 doi:10.1007/978-3-031-21550-6 | arXiv:1912.02167
- A user's guide to the local arithmetic of hyperelliptic curves (With A. Best, M. Bisatt, R. van Bommel, V. Dokchitser, O. Faraggi, S. Kunzweiler, A. Morgan, S. Muselli and S. Nowell) Bull. Lond. Math. Soc., 54(3), pp825–867, 2022 doi:10.1112/blms.12604 | arXiv:2007.01749
- Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction J. Number Theory 231, pp158–213, 2022 doi:10.1016/j.jnt.2020.09.021 | arXiv:1808.05479
- Variation of Tamagawa numbers of semistable abelian varieties in field extensions (with V. Dokchitser and A. Morgan) Math. Proc. Cam. Phil. Soc., 116, pp487–521, 2019 doi:10.1017/S0305004118000075 | arXiv:1405.3151
Preprints
- Local heights on hyperelliptic curves and quadratic Chabauty (with J. Duque-Rosero, S. Hashimoto and P. Spelier) arXiv:2401.05228
- Chabauty–Kim and the Section Conjecture for locally geometric sections (with T. Kumpitsch and M. Lüdtke) arXiv:2305.09462
- Towards Uniform Chabauty–Kim (with D. Corwin and M. Leonhardt) arXiv:2206.11085
- Galois sections and p-adic period mappings (with J. Stix) arXiv:2204.13674
- The local theory of unipotent Kummer maps and refined Selmer schemes (with N. Dogra) arXiv:1909.05734
Selected Talks
- Chabauty–Kim and the Section Conjecture for locally geometric sections Rational Points Workshop, Schney, 2023 Slides
- Computing Local Heights for Quadratic Chabauty Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting
- A partial finiteness theorem for the Selmer section set ADDING Conference, Athens GA, 2022
- Weights of Coleman functions and effective Chabauty–Kim Workshop on Rational Points and Galois Representations, Pittsburgh (online), 2021
- Galois sections and the Lawrence–Venkatesh method Queen Mary University Online Number Theory Seminar, 2020 Video | Slides
- Weight filtrations on Selmer schemes and effective non-abelian Chabauty Online 'Selminar' on Selmer Schemes, 2020 Video | Slides
- The Chabauty–Kim method Three-lecture mini-course at Paris 6, 2018
- Iterated integrals, Green's functions and fundamental groups Bristol Linfoot Number Theory Seminar, 2017
- Computing Tamagawa numbers of hyperelliptic curves ICTP Workshop on Hyperelliptic Curves, 2017 Slides
- Local heights on abelian varieties via non-abelian Bloch–Kato Selmer sets BIRS Workshop on Nilpotent Fundamental Groups, 2017 Video
- Non-abelian Bloch–Kato Selmer sets and an application to heights on abelian varieties 3rd Workshop on Interactions between Homotopy and Arithmetic, 2017 Slides | Handout