OpenAI · 040-01 · 2026-09-24 · Algebraic and complex geometry
Bloch’s conjecture for surfaces with p_g=0
preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026
Family 040. Bloch's conjecture for complex surfaces.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Bloch's conjecture: for every smooth connected projective complex surface with , the Albanese map on integral degree-zero zero-cycles is an isomorphism. This combines the new theorem with the classical theorem of Bloch, Kas, and Lieberman.
We prove Bloch's conjecture for smooth connected projective complex surfaces with : the Albanese homomorphism on integral degree-zero zero-cycles is an isomorphism.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.