Related papers: The $p$-completed cyclotomic trace in degree $2$

We extend the construction of A$_{\rm inf}$-cohomology by Bhatt-Morrow-Scholze to the context of log $p$-adic formal schemes over a log perfectoid base. In particular, using coordinates, we prove comparison theorems between log A$_{\rm…

In this paper, we study the Stokes phenomenon of the cyclotomic Knizhnik-Zamolodchikov equation, and prove that its two types of Stokes matrices satisfy the Yang-Baxter and reflection equations respectively. We then discuss its isomonodromy…

Inspired by the work [PA], we establish an explicit algebra isomorphism between the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ and a direct sum of matrix algebras over tensor products of degenerate cyclotomic Hecke…

In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical…

We show that Aomoto's $q$-deformation of de Rham cohomology arises as a natural cohomology theory for $\Lambda$-rings. Moreover, Scholze's $(q-1)$-adic completion of $q$-de Rham cohomology depends only on the Adams operations at each…

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomason's blow-up formula in algebraic K-theory to derived…

We prove two theorems on cohomologically complete complexes. These theorems are inspired by, and yield an alternative proof of, a recent theorem of P. Schenzel on complete modules.

Let kq denote the very effective cover of the motivic Hermitian K-theory spectrum. We analyze the ring of cooperations $\pi^\mathbb{R}_{**}(\text{kq} \otimes \text{kq})$ in the stable motivic homotopy category $\text{SH}(\mathbb{R})$,…

We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Pe\~na's algebras of cyclotomic type. Path algebras of affine type and…

Motivated by relating the representation theory of the split real and $p$-adic forms of a connected reductive algebraic group $G$, we describe a subset of $2^r$ orbits on the complex flag variety for a certain symmetric subgroup. (Here $r$…

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…

We give a new proof of the recent K\"unneth theorem for periodic topological cyclic homology (TP) of smooth and proper dg categories over perfect fields of characteristic p>0 due to Blumberg and Mandell. Our result is slightly stronger and…

We construct and study a t-structure on p-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t-structure. Our main tool is a new approach to p-typical cyclotomic…

We prove that the $p$-adically completed periodic topological cyclic homology of a DG category over a perfect field $k$ of characteristic $p>2$ is isomorphic to the ($p$-adically completed) periodic cyclic homology of a lifting of the DG…

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…

We compute the connective spectra of maps from $\mathbb{Z}$ to the Picard spectra of the spherical Witt vectors associated with perfect rings of characteristic $p$. As an application, we determine the connective spectrum of maps from…

We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by $\mathcal{C}_p$, $p \geq 2$, which are closely related to the vertex algebra of chiral differential operators on $SL(2)$ at level $-2+\frac{1}{p}$.…

We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic…

Let $p$ be an odd prime number and $\mathrm{j}_p$ the $p$-complete connective image of J spectrum. We establish an equivalence of cyclotomic $\mathbb{E}_\infty$-rings $\mathrm{THH}(\mathbb{Z})^{\wedge}_p \simeq…