Cohomology of the moduli stack of algebraic vector bundles

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2022-11-19

Department

Department of Applied Physics

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Language

en

Pages

25

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Advances in Mathematics, Volume 409, pp. 1-25

Abstract

Let Vectn 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⁎(Vectn,S) is freely generated by Chern classes c1,…,cn over E⁎(S) for any qcqs derived scheme S. Examples include all multiplicative localizing invariants.

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Funding Information: The first author was support by the Vilho, Yrjö and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters.The second author was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 896517. Publisher Copyright: © 2022 The Author(s)

Keywords

Algebraic K-theory, Derived algebraic geometry, Motives, Projective bundle formula

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DOI

10.1016/j.aim.2022.108638

Citation

Annala, T & Iwasa, R 2022, 'Cohomology of the moduli stack of algebraic vector bundles', Advances in Mathematics, vol. 409, 108638, pp. 1-25. https://doi.org/10.1016/j.aim.2022.108638

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https://urn.fi/URN:NBN:fi:aalto-202209145609

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[article-cris] Perustieteiden korkeakoulu / SCI