Year: 2026
Type: preprint
Abstract: Let $p$ be a fixed prime number and let $R$ be a $p$-quasisyntomic ring. We provide conditions for objects in the absolute prismatic site $R_\Prism$ to cover the final object in $\Shv(R_\Prism)$ and to admit finite self-coproducts in $R_\Prism$. More precisely, we introduce in $R_\Prism$ the so-called transversal objects, so that the coproduct of any object in $R_\Prism$ with a transversal object exists in $R_\Prism$. As an immediate generalization, we introduce the so-called relatively quasiregular semiperfectoid covers of $R$, whose prismatic cohomology (of $δ$-pairs, in the sense of Antieau-Krause-Nikolaus) produces objects in $R_\Prism$ that cover the final object in $\Shv(R_\Prism)$ and admit finite self-coproducts in $R_\Prism$.
Source: arXiv (Cornell University)
Author: Guo, Jingbang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167598507