An interpolation between special linear and general algebraic cobordism $\text{MSL}$ and $\text{MGL}$

Abstract

Conner and Floyd determined the torsion in the special unitary bordism $\text{MSU}$ back in the late 1960s. One of the ingredients of their work was an interpolation between $\text{MSU}$ and unitary bordism $\text{MU}$. In this work, we prove an exactly similar relation between the special, and general linear algebraic cobordism $\text{MSL}$, and $\text{MGL}$ in the stable motivic homotopy category over any Noetherian base scheme of finite Krull dimension. This gives a filtration of $\text{MGL}$ in terms of $\text{MSL}$, and the skeletal filtration of $\mathbb{P}^{\infty}$. Using that, we compute the first slice of $\text{MSL}$ over characteristic zero fields. We also compute the first line of the stable homotopy groups of $\text{MSL}$ over fields of characteristic zero.