Alexander Betts
Postdoctoral Researcher in Mathematics
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
- 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 (to appear) 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. (to appear) doi:10.1112/blms.12604 arXiv:2007.01749
- Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction J. Number Theory 231(2022), pp158--213 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(2019), pp487--521 doi:10.1017/S0305004118000075 arXiv:1405.3151
Preprints
- 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
- Local constancy of pro-unipotent Kummer maps arXiv:2203.03701
- Weight filtrations on Selmer schemes and the effective Chabauty--Kim method arXiv:2106.01218
- 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) arXiv:2106.10145
- The local theory of unipotent Kummer maps and refined Selmer schemes (with N. Dogra) arXiv:1909.05734
Selected Talks
- Grothendieck's section set and the Lawrence--Venkatesh method Connecticut Conference in Number Theory, 2022
- A partial finiteness theorem for the Selmer section set ADDING Conference, Athens GA, 2022
- Galois sections and the Lawrence--Venkatesh method Harvard Number Theory Seminar, 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
- Weight--monodromy and canonical paths on varieties Paris 6&7 Number Theory Seminar, 2020
- Non-abelian Kummer maps for curves Frankfurt Number Theory Seminar, 2019
- 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