arXiv subjects

Jingbang Guo

Publications and source records attributed to Jingbang Guo.

3 recordsLinked to original sources

arXiv2026

A Note on Topological Hochschild Homology Relative to $\Sphere_{W(k)}[x_0,x_1,\ldots,x_n]$

We explain the relation between the relative topological Hochschild homology $\THH(R/\Sphere_{W(k)}[x_0,\ldots,x_n])$ and the Nygaard completed Frobenius twisted relative prismatic cohomology $\widehat{\Prism}^{(1)}_{R/W(k)[x_0,\ldots,x_n]^\wedge}$, where $W(k)[x_0,x_1,\ldots,x_n]\rightarrow R$ is relatively quasiregular semiperfectoid. As an application, for $R=\Z_p[x]/(px)$, we compute $\pi_*\THH(R)^\wedge_p$ by descent along $\THH(R)^\wedge_p\rightarrow \THH(R/\Sphere_p[z,x])$, where $R=\Z_p[x]/(px)$ is regarded as an $\Einfty$-$\Sphere_p[z,x]$-algebra through $\Sphere_p[z,x]\xrightarrow{z\mapsto p,x\mapsto x}\Z_p[x]/(px)$.

math.AT↗

arXiv2026

A note on prismatic sites for p-quasisyntomic rings

Let $p$ be a fixed prime number and let $R$ be a $p$-quasisyntomic ring. In this note, we provide conditions for objects in the absolute prismatic site $R_\Prism$ to cover the final object in $\Shv(R_\Prism)$. More precisely, we introduce in $R_\Prism$ the so-called transversal objects, with which coproducts exist in $R_\Prism$. Immediately generalizing this, we introduce the so-called relatively quasiregular semiperfectoid covers of $R$, whose prismatic cohomology (of $\delta$-pairs, in the sense of Antieau-Krause-Nikolaus) would produce in $R_\Prism$ objects with which coproducts exist.

math.AG↗

arXiv2026

On Dual Algebras of Hopf Algebroids

We study the dual algebras of (discrete) Hopf algebroids. In particular, we understand comodules over a Hopf algebroid as (discrete) modules over its dual algebra.

math.RA↗