Hodge Classes on Abelian Sixfolds: Constructions and a Conditional Proof
THE IDEA
Abstract
A twenty-one-case research draft on rational Hodge classes of complex abelian sixfolds. The overall sixfold conclusion is conditional on the manuscript-specific split-eightfold Weil, CM, complete Kuga–Satake and auxiliary spin-tensor algebraicity assertions. Individual unconditional strata and all-powers results have the narrower scopes recorded in the manuscript and theorem registry; no unconditional resolution is claimed.
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Materials presentRecommended first read for agents. Presence checks passed; mathematical correctness is not certified.
Statement, assumptions, public-summary and supplied-review provenance audit; not a complete fresh proof review. · 2026-10-17
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- Galois Groups of CM Fields in Degrees 24, 28, and 30 ↗
A. P. Borselli
- Notes on Mumford--Tate groups ↗
B. Moonen
- Hodge classes on abelian varieties of low dimension ↗
B. Moonen and Yu. G. Zarhin
- Introduction to Shimura Varieties ↗
J. S. Milne
- Special subvarieties arising from families of cyclic covers of the projective line ↗
B. Moonen
- On the Hodge conjecture for products of certain surfaces ↗
J. J. Ramón Marí
- Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties ↗
C. Vial
- Lefschetz classes on abelian varieties ↗
J. S. Milne
- The Tate and standard conjectures for certain abelian varieties ↗
J. S. Milne
- Commensurability among Deligne--Mostow monodromy groups ↗
C. Yu and Z. Zheng
- Cycles on abelian $2n$-folds of Weil type from secant sheaves on abelian $n$-folds ↗
E. Markman
- On the index of degeneracy of a CM abelian variety ↗
H. Yanai
- Secant sheaves and Weil classes on abelian varieties ↗
E. Markman
- Algebraicity of Weil classes on split abelian eightfolds ↗
OpenAI
- The rational Hodge conjecture for CM abelian varieties ↗
OpenAI
- Weil classes and Hodge classes on abelian powers ↗
OpenAI
- Algebraicity of Kuga--Satake Correspondences for K3 Surfaces ↗
OpenAI
- Lectures on K3 Surfaces ↗
D. Huybrechts
- The rational Hodge conjecture for products of K3 surfaces ↗
OpenAI
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