An interpolation between special linear and general algebraic cobordism $\text{MSL}$ and $\text{MGL}$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912048686825472 |
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| author | Nandy, Ahina |
| author_facet | Nandy, Ahina |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15721 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An interpolation between special linear and general algebraic cobordism $\text{MSL}$ and $\text{MGL}$ Nandy, Ahina Algebraic Topology Algebraic Geometry 14F42, 55N22, 57R77 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. |
| title | An interpolation between special linear and general algebraic cobordism $\text{MSL}$ and $\text{MGL}$ |
| topic | Algebraic Topology Algebraic Geometry 14F42, 55N22, 57R77 |
| url | https://arxiv.org/abs/2310.15721 |