The Fixed-Part Lemma and Correspondence Rigidity
Abstract
We isolate and prove a fixed-part statement underlying correspondence rigidity for rational Hodge classes. Under a minimal semisimplicity and Tate-triviality package, the subspace of cohomology fixed by all algebraic correspondences is shown to be Tate, hence algebraic. This establishes the key lemma used in rigidity 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