arXiv subjects

Hyungseop Kim

Publications and source records attributed to Hyungseop Kim.

4 recordsLinked to original sources

arXiv2025

Thomason filtration via $T(1)$-local $\mathrm{TC}$

We construct a natural filtration on $T(1)$-local $\mathrm{TC}$ for any animated commutative rings using prismatic cohomology and descent theory. In the course of the construction, we also study some general properties of prismatic cohomology complexes over perfect prisms after inverting distinguished generators. The construction is intrinsic to $\mathrm{TC}$ and recovers Thomason's spectral sequence for $T(1)$-local algebraic K-theory via the cyclotomic trace map; as a consequence, we also recover the étale comparison for prismatic cohomology.

math.KT↗

arXiv2024

Some formal gluing diagrams for continuous K-theory

We study a construction of diagrams of dualizable presentable stable $\infty$-categories associated with certain fiber-cofiber sequences over rigid bases, which are sent by localizing invariants, in particular continuous K-theory, to limit diagrams. We apply this to investigate two closely related types of diagrams pertinent to the formal gluing situation; we recover Clausen--Scholze's gluing of continuous K-theory along punctured tubular neighborhoods via Efimov's nuclear module category, and we verify a continuous version of adelic descent statement for localizing invariants on dualizable categories.

math.KT↗

arXiv2023

Topological cyclic homology of Cartier smooth rings

We study algebraic K-theory, syntomic cohomology, and prismatic cohomology of Cartier smooth rings. As an application, we provide an alternative proof of Kelly-Morrow's generalization of the Geisser-Levine theorem computing $p$-adic algebraic K-theory of Cartier smooth local rings; our approach relies on the description of topological cyclic homology through the motivic filtration.

math.KT↗

arXiv2021

Adelic descent for K-theory

We prove an adelic descent result for localizing invariants: for each Noetherian scheme $X$ of finite Krull dimension and any localizing invariant $E$, e.g., algebraic K-theory of Bass-Thomason, there is an equivalence $E(X)\simeq \lim E(A^{\cdot}_{\text{red}}(X))$, where $A^{\cdot}_{\text{red}}(X)$ denotes Beilinson's semi-cosimplicial ring of reduced adeles on $X$. We deduce the equivalence from a closely related cubical descent result, which we prove by establishing certain exact sequences of perfect module categories over adele rings.

math.KT↗