Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 032-03. Weil classes and Hodge classes on abelian powers
Manuscript map · lines 3045–3054
OpenAI@2026-10-07#rem:oai-p-032-03
Authors: OpenAI. Family 032.
Title: Weil classes and Hodge classes on abelian powers.
Abstract: We prove the rational Hodge conjecture in every codimension on every self-power of a complex abelian sixfold with an imaginary-quadratic action and a compatible polarization whose rational homological Hermitian form is hyperbolic of signature $(3,3)$. We also prove it in every codimension on every self-power of a complex abelian variety of dimension at most five admitting an imaginary-quadratic action. Both results include nonsimple varieties and special periods with additional endomorphisms. The proof uses the companion theorem on the rational Hodge conjecture for CM abelian varieties.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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