The Lefschetz Standard Conjecture (B) for Abelian Varieties and Its Motivic Consequences
Abstract
We give a self-contained account of the Lefschetz standard conjecture (B) for complex abelian varieties and explain how this result propagates to André’s category of motivated motives. As a consequence, the existence of algebraic inverse Lefschetz operators holds unconditionally for all motives generated by abelian varieties. This provides the geometric input required for rigidity-based reductions of the Rational Hodge Conjecture.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 16 January 2026
- Document type
- Preprint