The Hodge standard conjecture for self-products of K3 surfaces
Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa
TL;DR
This paper proves the Hodge standard conjecture for self-products of K3 surfaces, advancing understanding of algebraic cycles and Hodge theory for these complex surfaces.
Contribution
It establishes the Hodge standard conjecture for squares and certain powers of K3 surfaces, building on previous work on CM liftings and the Tate conjecture.
Findings
Proved the Hodge standard conjecture for squares of K3 surfaces.
Extended the conjecture to all powers of certain K3 surfaces.
Connected the results to prior work on CM liftings and Tate conjecture.
Abstract
As an application of our previous work on CM liftings of K3 surfaces and the Tate conjecture, we prove the Hodge standard conjecture for squares of K3 surfaces. We also deduce the Hodge standard conjecture for all the powers of certain K3 surfaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology