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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.15721 |
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Table of Contents:
- 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.