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2019 Motivic analogues of $\mathsf{MO}$ and $\mathsf{MSO}$
Dondi Ellis
Ann. K-Theory 4(3): 345-382 (2019). DOI: 10.2140/akt.2019.4.345

Abstract

We construct algebraic unoriented and oriented cobordism, named MGLO and MSLO , respectively. MGLO is defined and its homotopy groups are explicitly computed, giving an answer to a question of Jack Morava. MSLO is also defined and its coefficients are explicitly computed after completing at a prime p . Similarly to MSO , the homotopy type of MSLO depends on whether the prime p is even or odd. Finally, a computation of a localization of the homotopy groups of MGLR is given.

Citation

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Dondi Ellis. "Motivic analogues of $\mathsf{MO}$ and $\mathsf{MSO}$." Ann. K-Theory 4 (3) 345 - 382, 2019. https://doi.org/10.2140/akt.2019.4.345

Information

Received: 16 March 2017; Revised: 7 January 2019; Accepted: 23 January 2019; Published: 2019
First available in Project Euclid: 3 January 2020

MathSciNet: MR4043463
Digital Object Identifier: 10.2140/akt.2019.4.345

Subjects:
Primary: 14F42
Secondary: 19D99 , 55N22 , 55N91 , 55P15 , 55P42

Keywords: bordism and cobordism theories , classification of homotopy type , equivariant homology and cohomology , formal group laws , motivic cohomology , motivic homotopy theory , spectra , stable homotopy theory

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.4 • No. 3 • 2019
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