Motivic Analogues of MO and MSO

Abstract

This thesis makes progress in computing the coefficients of Algebraic Hermitian Cobordism (MGLR), a motivic Z/2-equivariant spectrum constructed by P. Hu, I. Kriz, and K. Ormsby. In the process of my research, I realized it would be possible to construct motivic analogues of unoriented and oriented cobordism, which I refer to as MGLO and MSLO respectively. In chapters 2-3 of my thesis, I construct MGLO and MLSO and give a concrete description of the homotopy groups of each of them. In particular, my work on MGLO gives an answer to a question of Jack Morava. Using the tools of Tate cohomology and my computation of the coefficients of MGLO, the thesis ends with a computation of a localization of the homotopy groups of MGLR.