相关论文: Logarithmic prismatic cohomology, motivic sheaves,…
We study the logarithmic syntomic cohomology of fine and saturated log schemes and its realization in the logarithmic motivic stable homotopy category $\mathrm{logSH}(\mathrm{pt}_\mathbb{N})$ of a log point. We prove that logarithmic…
For a regular immersion of schemes $Z\to X$ and a cohomology theory of fs log schemes, we formulate the logarithmic Gysin sequence using the "logarithmic compactification" $(\mathrm{Bl}_Z X,E)$ instead of the open complement $X-Z$, where…
We continue to study the logarithmic prismatic cohomology defined by the first author, and complete the proof of the de Rham comparison and \'etale comparison generalizing those of Bhatt and Scholze. We prove these comparisons for a derived…
We develop a theory of motives with compact support for logarithmic schemes over a field. Starting from the notion of finite logarithmic correspondences with compact support, we define the logarithmic motive with compact support analogous…
This paper provides the technical tools needed in ongoing work of the authors to compute p-adic \'etale Abel-Jacobi maps in order to obtain explicit reciprocity laws for GSp4. In particular, we define and study syntomic polynomial…
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 correspondences, the dividing Nisnevich topology on log…
We show a comparison theorem between log prismatic cohomology and log crystalline cohomology for a $p$-adic formal scheme with semistable reduction. Combined with the prismatic-\'etale comparison theorem recently proved by Tian, this…
In this paper, we study a Gysin triangle in the category of motives with modulus. We can understand this Gysin triangle as a motivic lift of the Gysin triangle of log-crystalline cohomology due to Nakkajima and Shiho. After that we compare…
The aim of this paper is to connect two important and apparently unrelated theories: motivic homotopy theory and ramification theory. We construct motivic homotopy categories over a qcqs base scheme $S$, in which cohomology theories with…
Log prismatic cohomology theory developed by Koshikawa-Yao involves coefficient objects, called log prismatic $F$-crystals. In this paper, we construct and study realization functors from the category of log prismatic $F$-crystals to the…
In this article, we analyze the connection between the Log De Rham Cohomology of an fs (not necessary log smooth) log scheme $Y$ over $\mathbb C$ (for $Y$ admitting an exact closed immersion into an fs log smooth log scheme over $\mathbb…
The proof of the coincidence of the Gysin morphism in motivic cohomology and the usual pushout on Chow groups has been improved (see Lemma 3.3 and Proposition 3.11)
For a smooth $p$-adic formal scheme over the ring of integers of a perfectoid field of mixed characteristic $(0,p)$ containing all $p$-power roots of unity, we prove that the prismatic cohomology of a locally finite free prismatic crystal…
We establish a comparison isomorphism between prismatic cohomology and derived de Rham cohomology respecting various structures, such as their Frobenius actions and filtrations. As an application, when $X$ is a proper smooth formal scheme…
The aim of this paper is to show that Besser syntomic cohomology is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous constructions, we exhibit a simple representability criterion and we…
We apply our previous results on ``saturated descent'' to express a wide range of logarithmic cohomology theories in terms of the infinite root stack. Examples include the log cotangent complex, Rognes' log topological cyclic homology, and…
We consider slice filtrations in logarithmic motivic homotopy theory. Our main results establish conjectured compatibilities with the Beilinson, BMS, and HKR filtrations on (topological, log) Hochschild homology and related invariants. In…
This work is dedicated to the construction of a new motivic homotopy theory for (log) schemes, generalizing Morel-Voevodsky's (un)stable $\mathbb{A}^1$-homotopy category. Our framework can be used to represent log topological Hochschild and…
In this article, we prove the comparison theorem between the relative log de Rham-Witt cohomology and the relative log crystalline cohomology for a log smooth saturated morphism of fs log schemes satisfying certain condition. Our result…
Le Stum and Quir\'os proved the formal Poincar\'e lemma in crystalline cohomology of higher level using the jet complex, and applied it to give a de Rham interpretation of this cohomology. In this article, we prove the logarithmic version…