相关论文: A Universal HKR Theorem

We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg (HKR) filtration. This involves endowing these objects with extra structure, built on…

In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded…

Hodge-filtered derived de Rham cohomology of a ring $R$ can be described (up to completion and shift) as the graded pieces of the even filtration on $\mathrm{HC}^-(R)$. In this paper we show a deformation of this result: If $R$ admits a…

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the…

We refine several results of Bhatt-Morrow-Scholze on THH to THR. In particular, we compute THR of perfectoid rings. This will be useful for establishing motivic filtrations on real topological Hochschild and cyclic homology of quasisyntomic…

Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural…

Arone and Lesh constructed and studied spectrum level filtrations that interpolate between connective (topological or algebraic) K-theory and the Eilenberg-MacLane spectrum for the integers. In this paper we consider (global) equivariant…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this…

In this paper we examine certain filtrations of topological Hochschild homology and topological cyclic homology. As an example we show how the filtration with respect to a nilpotent ideal gives rise to an analog of a theorem of Goodwillie…

We discuss filtrations arising from de Rham-type cohomology theories for $E_\infty$ rings and $E_n$ rings. Examples include the HKR filtration on relative topological Hochschild homology, the Hodge filtration on $E_\infty$ infinitesimal…

We compare several different notions of filtered derived commutative ring, discussing HKR-filtered Hochschild homology, Hodge-filtered de Rham cohomology, and the lesser-known Hodge-filtered infinitesimal cohomology. Our main result is that…

We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid…

We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived…

In this paper, we introduce a notion of derived involutive algebras in $ C_2 $-Mackey functors which simultaneously generalize commutative rings with involution and the (non-equivariant) derived algebras of Bhatt--Mathew and Raksit. We show…

We prove a Hochschild-Kostant-Rosenberg theorem ("the HKR theorem") which computes the factorization homology of certain smooth commutative ring spectra. In doing so we fix and generalize a THH computation which was first conceived as the…

Using topological cyclic homology, we give a refinement of Beilinson's $p$-adic Goodwillie isomorphism between relative continuous $K$-theory and cyclic homology. As a result, we generalize results of Bloch-Esnault-Kerz and Beilinson on the…

Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified…

We demonstrate that a conjecture of Teh which relates the niveau filtration on Borel-Moore homology of real varieties and the images of generalized cycle maps from reduced Lawson homology is false. We show that the niveau filtration on…