Cohomology of the moduli stack of algebraic vector bundles

Abstract

Let $\mathcal{V}{\mathrm{ect}}_n$ be the moduli stack of vector bundles of rank $n$ on schemes. We prove that, if $E$ is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies the projective bundle formula, then $E^{\ast }(\mathcal{V}{\mathrm{ect}}_{n,S})$ is freely generated by Chern classes $c_1,\dots ,c_n$ over $E^{\ast }(S)$ for any scheme $S$. Examples include all multiplicative localizing invariants.

arXiv comment17 pages. Final version + footnotes

References in corpus (10)

• Higher Topos Theory
• A universal characterization of higher algebraic K-theory
• Universality of multiplicative infinite loop space machines
• On the K-theory of pullbacks
• Modules over algebraic cobordism
• Hodge theory of classifying stacks
• Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs
• Algebraic K-theory of quasi-smooth blow-ups and cdh descent
• A bivariant Yoneda lemma and $(\infty ,2)$-categories of correspondences
• A motivic homotopy theory without ${\mathbb{A}}^1$ invariance

Cited by in corpus (1)

• ${\mathbb{A}}^1$-invariance of localizing invariants