An Alternative to Spherical Witt Vectors
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912232542044160 |
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| author | Nikolaus, Thomas Yakerson, Maria |
| author_facet | Nikolaus, Thomas Yakerson, Maria |
| contents | We give a direct construction of the ring spectrum of spherical Witt vectors of a perfect $\mathbb{F}_p$-algebra R as the completion of the spherical monoid algebra $\mathbb{S}[R]$ of the multiplicative monoid $(R,\cdot)$ at the ideal $I = \mathrm{fib}(\mathbb{S}[R] \to R)$. This generalizes a construction of Cuntz and Deninger. We also use this to give a description of the category of p-complete modules over the spherical Witt vectors and a universal property for spherical Witt vectors as an $\mathbb{E}_1$-ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Alternative to Spherical Witt Vectors Nikolaus, Thomas Yakerson, Maria Algebraic Topology Commutative Algebra Algebraic Geometry Number Theory We give a direct construction of the ring spectrum of spherical Witt vectors of a perfect $\mathbb{F}_p$-algebra R as the completion of the spherical monoid algebra $\mathbb{S}[R]$ of the multiplicative monoid $(R,\cdot)$ at the ideal $I = \mathrm{fib}(\mathbb{S}[R] \to R)$. This generalizes a construction of Cuntz and Deninger. We also use this to give a description of the category of p-complete modules over the spherical Witt vectors and a universal property for spherical Witt vectors as an $\mathbb{E}_1$-ring. |
| title | An Alternative to Spherical Witt Vectors |
| topic | Algebraic Topology Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2405.09606 |