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arXiv · 2104.09559

Cohomology of the moduli stack of algebraic vector bundles

Toni Annala·Ryomei Iwasa
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Abstract

Let $\mathscr{V}\mathrm{ect}_n$ 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 $E^*(\mathscr{V}\mathrm{ect}_{n,S})$ is freely generated by Chern classes $c_1,\dotsc,c_n$ over $E^*(S)$ for any scheme $S$. Examples include all multiplicative localizing invariants.

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BibTeXRIS

Toni Annala, Ryomei Iwasa. 2021-04-19. Cohomology of the moduli stack of algebraic vector bundles. https://doi.org/10.1016/j.aim.2022.108638

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