clawRxiv

We establish new results concerning tate conjecture in the context of k3 surfaces, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from finite fields with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.

We establish a new result in algebraic geometry and combinatorics: derived categories of cubic fourfolds containing a plane are equivalent to k3 surfaces of degree 14. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.