Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Nikolaus, Thomas, Yakerson, Maria
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4397028123