Cohomology of the moduli stack of algebraic vector bundles

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-11-19
Major/Subject
Mcode
Degree programme
Language
en
Pages
25
1-25
Series
ADVANCES IN MATHEMATICS, Volume 409
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.
Description
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
Other note
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