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

We show that the abstract equivalence of categories, called Cartier transform, between crystals on the q-crystalline and prismatic sites can be locally identified with the explicit local q-twisted Simpson correspondence. This establishes…

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally…

In this paper we continue our study of logarithmic topological Hochschild homology. We show that the inclusion of the connective Adams summand into the p-local complex connective K-theory spectrum, equipped with suitable log structures, is…

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence…

Simplicial complexes X provide commutative rings A(X) via the Stanley-Reisner construction. We calculated the cotangent cohomology, i.e., T1 and T2 of A(X) in terms of X. These modules provide information about the deformation theory of the…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the "slice" condition. Our new construction is based on local…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

Topological cyclic homology is a refinement of Connes--Tsygan's cyclic homology which was introduced by B\"okstedt--Hsiang--Madsen in 1993 as an approximation to algebraic $K$-theory. There is a trace map from algebraic $K$-theory to…

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…

We introduce the notions of Koszul $N$-complex, $\check{\mathrm{C}}$ech $N$-complex and telescope $N$-complex, explicit derived torsion and derived completion functors in the derived category $\mathbf{D}_N(R)$ of $N$-complexes using the…

Let $p$ be a prime. We resolve a question posed by Min\'a\v{c}-Rogelstad-T\^an. We relate the Zassenhaus and the lower central series of pro-$p$ groups under a torsion-freeness condition. We also study graph products of (pro-$p$) groups…

The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$.…

Given a Hamiltonian action of a proper symplectic groupoid (for instance, a Hamiltonian action of a compact Lie group), we show that the transverse momentum map admits a natural constant rank stratification. To this end, we construct a…

In this article, we suggest a categorification procedure in order to capture an analogy between Crystalline Grothendieck-Lefschetz trace formula and the cyclotomic trace map $K\rightarrow TC$ from the algebraic $K$-theory to the topological…

For two representations of some local division algebra, congruent modulo $l$, giving rise to two Harris-Taylor local systems on the corresponding Newton strata of the special fiber of a KHT Shimura varieties, we prove that the $l$-torsion…

In this article we are concerned with how to compute the cohomology ring of a symplectic quotient by a circle action using the information we have about the cohomology of the original manifold and some data at the fixed point set of the…

We compute the first cohomology group of the symmetric algebra of the universal \'etale $p$-adic local system on the tower of coverings of Drinfeld's $p$-adic half-plane. The result takes a factorized form, using the $p$-adic Langlands…

We develop a categorical and algebro-geometric treatment of localization for cohomological theories endowed with an open--closed recollement. Starting from a class on a space whose restriction to the open complement vanishes, we show that…