3 citations · 12 across the 17 of their papers we have counts for
19 papers
Six-functor formalism for Kummer étale cohomology of log schemes
Doosung Park
We establish a Grothendieck six-functor formalism for Kummer étale cohomology including Poincaré duality for every separated vertical exact log smooth morphism of noetherian fs log…
The logarithmic - and -topologies
Nikolai Opdan, Doosung Park, Paul Arne Østvær
We introduce the - and -topologies in the context of logarithmic geometry and discuss their applications to log étale cohomology, log differential forms, and log motives.
Log syntomic cohomology of truncated polynomials and coordinate axes
Doosung Park, Paul Arne Østvær
We study the logarithmic syntomic cohomology of fine and saturated log schemes and its realization in the logarithmic motivic stable homotopy category $\mathrm{logSH}(\mathrm{pt}_\…
On the log motivic stable homotopy groups
Doosung Park
We compare the log motivic stable homotopy category and the usual motivic stable homotopy category over a perfect field admitting resolution of singularities. As a consequence, we…
Logarithmic Prismatic Cohomology via Logarithmic THH
Federico Binda, Tommy Lundemo, Doosung Park +1
Inspired by Bhatt-Morrow-Scholze's work on , we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\…
Motivic real topological Hochschild spectrum
Doosung Park
We define real topological Hochschild homology of separated log schemes with involutions. We show that real topological Hochschild homology is -inv…
Log motivic Gysin isomorphisms
Doosung Park
In this article, we construct the Gysin isomorphisms in the axiomatic motivic setting for fs log schemes. We formulate the purity transformations for log smooth morphisms. We show…
Inverting log blow-ups in log geometry
Doosung Park
In the category of log schemes, it is unclear how to define the blow-ups for non-strict closed immersions. In this article, we introduce the notion of divided log spaces. We obtain…
Logarithmic motivic homotopy theory
Federico Binda, Doosung Park, Paul Arne Østvær
This work is dedicated to the construction of a new motivic homotopy theory for (log) schemes, generalizing Morel-Voevodsky's (un)stable -homotopy category. Our frame…
A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology
Federico Binda, Tommy Lundemo, Doosung Park +1
This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of derived pre-log r…
Real topological Hochschild homology of schemes
Jens Hornbostel, Doosung Park
We prove that real topological Hochschild homology THR for schemes with involution satisfies base change and descent for the Z/2-isovariant étale topology. As an application, we pr…
-homotopy theory of log schemes
Doosung Park
We construct the -local stable motivic homotopy categories of fs log schemes. For schemes with the trivial log structure, our construction is equivalent to the origin…
Triangulated categories of logarithmic motives over a field
Federico Binda, Doosung Park, Paul Arne Østvær
In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log c…
Motivic interpretation of Albanese varieties of smooth varieties
Doosung Park
For every noetherian smooth and separated scheme over an algebraically closed field, we define its derived Albanese in Voevodsky's triangulated category of effective Nisnevich moti…
Construction of triangulated categories of motives using the localization property
Doosung Park
Using the localization property, we construct a triangulated category of motives over quasi-projective T-schemes for any coefficient where T is a noetherian separated scheme, and w…
Description of mixed motives
Doosung Park
Assuming the Künneth type standard conjecture, we propose a way to describe objects of mixed motives explicitly. We study their formal properties, and we associate mixed motives to…
Intermediate Jacobians and the slice filtration
Doosung Park
For every -dimensional smooth projective variety over , the motive is expected to admit a Chow-Künneth decomposition . I…
Equivariant cd-structures and descent theory
Doosung Park
We construct the equivariant version of cd-structures, and we develop descent theory for topologies comes from equivariant cd-structures. In particular, we reprove several results…
Triangulated categories of motives over fs log schemes
Doosung Park
We introduce the notion of log motivic triangulated categories, which is the theoretical framework for understanding the motivic aspect of cohomology theories for fs log schemes. T…