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THE UNIT MAP OF THE ALGEBRAIC SPECIAL LINEAR COBORDISM SPECTRUM

Part of: (Co)homology theory

Published online by Cambridge University Press:  24 December 2019

Maria Yakerson Open the ORCID record for Maria Yakerson [Opens in a new window]
Maria Yakerson*
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Universitätstr. 31, 93040 Regensburg, Germany (maria.yakerson@ur.de) URL: https://www.muramatik.com
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Abstract

In the joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^{1}$-loop spaces of motivic Thom spectra using the technique of framed correspondences. This result allows us to express non-negative $\mathbb{G}_{m}$-homotopy groups of motivic Thom spectra in terms of geometric generators and relations. Using this explicit description, we show that the unit map of the algebraic special linear cobordism spectrum induces an isomorphism on $\mathbb{G}_{m}$-homotopy sheaves.

Keywords

framed correspondencesmotivic homotopy groups

MSC classification

Primary: 14F42: Motivic cohomology; motivic homotopy theory
Secondary: 14F99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 6 , November 2021 , pp. 1905 - 1930
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Copyright
© Cambridge University Press 2019

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Footnotes

The author was supported by SFB/TR 45 ‘Periods, moduli spaces and arithmetic of algebraic varieties’.

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