Recent publications/preprints:


(arxiv) Hasse principle for Kummer varieties in the case of generic 2-torsion, Sept 2023

(arxiv) Parity of ranks of Jacobians of curves, with V. Dokchitser, H. Green and A. Konstantinou, Nov 2022

(arxiv) Field change for the Cassels-Tate pairing and applications to class groups, with A. Smith, June 2022

(arxiv) The Cassels-Tate pairing for finite Galois modules, with A. Smith, March 2021 (updated June 2022)

(arxiv) The 4-rank of class groups of K(\sqrt{n}) , with P. Koymans and H. Smit, January 2021

Accepted papers:

(arxiv) 2-Selmer parity for hyperelliptic curves in quadratic extensions, Proc. London Math. Soc. 127 (2023), no. 5, 1507-1576 (abs)

(arxiv) Isogenies between abelian varieties with good ordinary reduction, appendix to
     V. Dokchitser, C. Maistret "On the parity conjecture for abelian surfaces", Proc. London Math. Soc., 127 (2023), no. 2, 295-365

(arxiv) A note on hyperelliptic curves with ordinary reduction over 2-adic fields, with V. Dokchitser, J. Number Theory 244 (2023), 264-278 (abs)

(arxiv) Arithmetic of hyperelliptic curves over local fields, with T. Dokchitser, V. Dokchitser and C. Maistret, Math. Ann. 385 (2023), 1213–1322. (abs)

(arxiv) On 2-Selmer groups of twists after quadratic extension, with R. Paterson, J. London Math. Soc. 105 (2022), 1110-1166 (abs)

(arxiv) A user's guide to the local arithmetic of hyperelliptic curves, with A. Best, L.A. Betts, M. Bisatt, R. van Bommel, V. Dokchitser, O. Faraggi, S. Kunzweiler, C. Maistret, S. Muselli, S. Nowell,
Bull. Lond. Math. Soc. 54 (2022), no. 3, 825--867 (abs)

(arxiv) Tate module and bad reduction, with T. Dokchitser and V. Dokchitser, Proc. Amer. Math. Soc. 149 (2021), 1361-1372 (abs)

(arxiv) Quadratic twists of abelian varieties and disparity in Selmer ranks, Algebra and Number Theory 13 (2019), no. 4, 839-899 (abs)

(arxiv) Semistable types of hyperelliptic curves, with T. Dokchitser, V. Dokchitser and C. Maistret, Contemporary Math., vol. 724 (2019)

(arxiv) Integral module structure of Λ_{A/K} for Jacobians of semistable hyperelliptic curves of genus 2, with V. Dokchitser, appendix to
     A. Betts and V. Dokchitser "Variation of Tamagawa numbers of semistable abelian varieties in field extensions", Math. Proc. Cam. Phil. Soc., 166 (2019), no. 3, 487-521 (abs)