Milnor excision for motivic spectra

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Milnor excision for motivic spectra. / Elmanto, Elden; Hoyois, Marc; Iwasa, Ryomei; Kelly, Shane.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2021, No. 779, 2021, p. 223-235.

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

Harvard

Elmanto, E, Hoyois, M, Iwasa, R & Kelly, S 2021, 'Milnor excision for motivic spectra', Journal fur die Reine und Angewandte Mathematik, vol. 2021, no. 779, pp. 223-235. https://doi.org/10.1515/crelle-2021-0040

APA

Elmanto, E., Hoyois, M., Iwasa, R., & Kelly, S. (2021). Milnor excision for motivic spectra. Journal fur die Reine und Angewandte Mathematik, 2021(779), 223-235. https://doi.org/10.1515/crelle-2021-0040

Vancouver

Elmanto E, Hoyois M, Iwasa R, Kelly S. Milnor excision for motivic spectra. Journal fur die Reine und Angewandte Mathematik. 2021;2021(779):223-235. https://doi.org/10.1515/crelle-2021-0040

Author

Elmanto, Elden ; Hoyois, Marc ; Iwasa, Ryomei ; Kelly, Shane. / Milnor excision for motivic spectra. In: Journal fur die Reine und Angewandte Mathematik. 2021 ; Vol. 2021, No. 779. pp. 223-235.

Bibtex

@article{4c099b55f7464134a78c3a7af327098a,
title = "Milnor excision for motivic spectra",
abstract = "We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal IA{I\subset A} isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I{A/I} that are identified over B/IB{B/IB}. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's {\'e}tale motives over schemes of finite virtual cohomological dimension.",
author = "Elden Elmanto and Marc Hoyois and Ryomei Iwasa and Shane Kelly",
year = "2021",
doi = "10.1515/crelle-2021-0040",
language = "English",
volume = "2021",
pages = "223--235",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",
number = "779",

}

RIS

TY - JOUR

T1 - Milnor excision for motivic spectra

AU - Elmanto, Elden

AU - Hoyois, Marc

AU - Iwasa, Ryomei

AU - Kelly, Shane

PY - 2021

Y1 - 2021

N2 - We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal IA{I\subset A} isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I{A/I} that are identified over B/IB{B/IB}. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's étale motives over schemes of finite virtual cohomological dimension.

AB - We prove that the ∞{\infty}-category of motivic spectra satisfies Milnor excision: if A→B{A\to B} is a morphism of commutative rings sending an ideal IA{I\subset A} isomorphically onto an ideal of B, then a motivic spectrum over A is equivalent to a pair of motivic spectra over B and A/I{A/I} that are identified over B/IB{B/IB}. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's étale motives over schemes of finite virtual cohomological dimension.

UR - http://www.scopus.com/inward/record.url?scp=85113301416&partnerID=8YFLogxK

U2 - 10.1515/crelle-2021-0040

DO - 10.1515/crelle-2021-0040

M3 - Journal article

AN - SCOPUS:85113301416

VL - 2021

SP - 223

EP - 235

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 779

ER -

ID: 284176499