Cohomology of the moduli stack of algebraic vector bundles

Toni Annala; Ryomei Iwasa

doi:10.1016/j.aim.2022.108638

Cohomology of the moduli stack of algebraic vector bundles

Toni Annala
, Ryomei Iwasa^*

^*Corresponding author for this work

University of British Columbia
University of Copenhagen

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

149 Downloads (Pure)

Abstract

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 c₁,…,c_n over E^⁎(S) for any qcqs derived scheme S. Examples include all multiplicative localizing invariants.

Original language	English
Article number	108638
Pages (from-to)	1-25
Number of pages	25
Journal	Advances in Mathematics
Volume	409
DOIs	https://doi.org/10.1016/j.aim.2022.108638
Publication status	Published - 19 Nov 2022
MoE publication type	A1 Journal article-refereed

Funding

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.

Keywords

Algebraic K-theory
Derived algebraic geometry
Motives
Projective bundle formula

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10.1016/j.aim.2022.108638Licence: CC BY

Cohomology of the moduli stack of algebraic vector bundlesFinal published version, 400 KBLicence: CC BY

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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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AU - Iwasa, Ryomei

N1 - 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)

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N2 - 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.

AB - 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.

KW - Algebraic K-theory

KW - Derived algebraic geometry

KW - Motives

KW - Projective bundle formula

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JF - Advances in Mathematics

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ER -

Cohomology of the moduli stack of algebraic vector bundles

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