An explicit construction of a rank 2 vector bundle on projective 3-space

Atiyah and Rees proved that the Chern classes and a mod 2 invariant, named the alpha invariant, classifies all rank 2 topological vector bundles on P3. They also showed that a construction by Horrocks provides algebraic representatives for all topological rank 2 bundles. However, Horrocks’ construction is non-explicit. The goal of this talk is to construct an algebraic rank 2 bundle on P3 with trivial Chern classes and non-trivial alpha invariant. We will use methods from motivic homotopy theory to construct an explicit algebraic description of the bundle. This is joint work with Jean Fasel.