| Sep 13, 2026 |
A new erratum to A note on Fourier–Mukai partners of abelian varieties over positive characteristic fields is now posted on the publications page. The converse implication in Proposition 4.5 of that paper is false — Ogus’s Torelli theorem gives a bijection on isomorphism classes, which does not realize a prescribed crystalline isometry — and the erratum gives a counterexample over \(\overline{\mathbb{F}}_5\): supersingular abelian surfaces \(A \not\cong B\) related by a degree-2 isogeny, with isomorphic abelian crystals but inequivalent derived categories. The surface theorem, Theorem 4.6, does not use the erroneous converse and stands unchanged. This note replaces the earlier addendum, whose strong-approximation argument is withdrawn.
|
| Sep 12, 2026 |
Full-text HTML versions of my papers are now available alongside the PDFs — look for the HTML button on the publications page. They are generated from the LaTeX sources with LaTeXML, the same converter arXiv uses, so the mathematics is real text rather than images: it reflows on a phone, and it can be searched, copied and read by a screen reader.
|
| Aug 31, 2026 |
I have added an Ongoing Papers section to this page, listing work that is written up or nearly written up but not yet posted. As open problems are increasingly attacked with AI assistance, it seems worth stating publicly what is already in preparation, so that the effort is not duplicated. Each entry gives its current status, the month it was last updated, and an abstract.
|