Cohomology of the moduli stack of algebraic vector bundles

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Standard

Cohomology of the moduli stack of algebraic vector bundles. / Annala, Toni; Iwasa, Ryomei.

In: Advances in Mathematics, Vol. 409, 108638, 2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

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

APA

Annala, T., & Iwasa, R. (2022). Cohomology of the moduli stack of algebraic vector bundles. Advances in Mathematics, 409, [108638]. https://doi.org/10.1016/j.aim.2022.108638

Vancouver

Annala T, Iwasa R. Cohomology of the moduli stack of algebraic vector bundles. Advances in Mathematics. 2022;409. 108638. https://doi.org/10.1016/j.aim.2022.108638

Author

Annala, Toni ; Iwasa, Ryomei. / Cohomology of the moduli stack of algebraic vector bundles. In: Advances in Mathematics. 2022 ; Vol. 409.

Bibtex

@article{bcd4aac1f09f4b8985a5c21fa5147ed4,
title = "Cohomology of the moduli stack of algebraic vector bundles",
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.",
keywords = "Algebraic K-theory, Derived algebraic geometry, Motives, Projective bundle formula",
author = "Toni Annala and Ryomei Iwasa",
note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",
year = "2022",
doi = "10.1016/j.aim.2022.108638",
language = "English",
volume = "409",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Cohomology of the moduli stack of algebraic vector bundles

AU - Annala, Toni

AU - Iwasa, Ryomei

N1 - Publisher Copyright: © 2022 The Author(s)

PY - 2022

Y1 - 2022

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

UR - http://www.scopus.com/inward/record.url?scp=85136586317&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2022.108638

DO - 10.1016/j.aim.2022.108638

M3 - Journal article

AN - SCOPUS:85136586317

VL - 409

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 108638

ER -

ID: 318816134