Vol. 4, No. 3, 2019

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Motivic analogues of $\mathsf{MO}$ and $\mathsf{MSO}$

Dondi Ellis

Vol. 4 (2019), No. 3, 345–382
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.

Keywords
motivic cohomology, motivic homotopy theory, bordism and cobordism theories, formal group laws, equivariant homology and cohomology, classification of homotopy type, stable homotopy theory, spectra
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 19D99, 55N22, 55N91, 55P15, 55P42
Milestones
Received: 16 March 2017
Revised: 7 January 2019
Accepted: 23 January 2019
Published: 17 December 2019
Authors
Dondi Ellis
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States