Related papers: Perfect even modules and the even filtration
Given a finitely-generated group $\pi$ and a linear algebraic group $G$, the representation variety Hom$(\pi,G)$ has a natural filtration by the characteristic varieties associated to a rational representation of $G$. Its algebraic…
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…
Milne's correcting factor, which appears in the Zeta-value at $s=n$ of a smooth projective variety $X$ over a finite field $\mathbb{F}_q$, is the Euler characteristic of the derived de Rham cohomology of $X/\mathbb{Z}$ modulo the Hodge…
We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…
A conjecture of Voisin states that two points on a smooth projective complex variety whose algebra of holomorphic forms is generated in degree 2 are rationally equivalent to each other if and only if their difference lies in the third step…
The goal of this paper is to study non-$\mathbb{A}^1$-invariant motivic cohomology, recently defined by Elmanto, Morrow, and the first-named author, for smooth schemes over possibly non-discrete valuation rings. We establish that the cycle…
Let $R$ be a discrete valuation ring of mixed characteristics $(0,p)$, with finite residue field $k$ and fraction field $K$, let $k'$ be a finite extension of $k$, and let $X$ be a regular, proper and flat $R$-scheme, with generic fibre…
We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an…
Flat modules play an important role in the study of the category of modules over rings and in the characterization of some classes of rings. We study the e-flatness for semimodules introduced by the first author using his new notion of…
We introduce the operation of even periodization on nonconnective spectral stacks. We show how to recover from it the even filtration of Hahn-Raksit-Wilson, and (a Nygaard-completion of) the filtered prismatization stack of Bhatt-Lurie and…
We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the $\gamma$-filtration.…
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…
We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this…
We consider the principal block of category O and its graded version. On the space of homomorphisms from a Verma module to an indecomposable tilting module we may define natural filtrations following Andersen. The arguments given in this…
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to…
We study the Milnor-Witt motives which are a finite direct sum of $\mathbb{Z}(q)[p]$ and $\mathbb{Z}/\eta(q)[p]$. We show that for MW-motives of this type, we could determine an MW-motivic cohomology class in terms of a motivic cohomology…
In this paper we prove the following results (via a unified approach) for all sufficiently large $n$: (i) [$1$-factorization conjecture] Suppose that $n$ is even and $D\geq 2\lceil n/4\rceil -1$. Then every $D$-regular graph $G$ on $n$…
We first show the existence of a weight filtration on the equivariant cohomology of real algebraic varieties equipped with the action of a finite group, by applying group cohomology to the dual geometric filtration. We then prove the…
We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This recovers for cycles of low codimensions on smooth projective varieties…
We establish the flat cohomology version of the Gabber-Thomason purity for \'{e}tale cohomology: for a complete intersection Noetherian local ring $(R, \mathfrak{m})$ and a commutative, finite, flat $R$-group $G$, the flat cohomology…