Cohomology of the moduli stack of algebraic vector bundles

Let Vect(n) be the moduli stack of vector bundles of rank n on derived schemes. We prove that, if E is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies projective bundle formula, then E*(Vect(n,S)) is freely generated by Chern classes c(1), . . . ,c(n) over E*(S) for any qcqs derived scheme S. Examples include all multiplicative localizing invariants. (C) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This study proves that on derived schemes, for a Zariski sheaf of ring spectra E equipped with finite quasi-smooth transfers and satisfying projective bundle formula, E*(Vect(n,S)) can be freely generated by Chern classes c(1), . . . ,c(n) over E*(S).