Related papers: Chow Groups: A Structure Theorem, RIEMANN-ROCH wit…

We study the Chow ring of the moduli stack $\mathfrak{M}_{g,n}$ of prestable curves and define the notion of tautological classes on this stack. We extend formulas for intersection products and functoriality of tautological classes under…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

In this paper, our aim is twofold: First, by using the technique of gluing semigroups, we give infinitely many families of a projective closure with the Cohen-Macaulay (Gorenstein) property. Also, we give an effective technique for…

In Grauert's paper [G] it is noted that finite dimensionality of cohomology groups sometimes implies vanishing of these cohomomogy groups. Later on Laufer formulated a zero or infinity law for the cohomology groups of domains in Stein…

The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow ring of the moduli space of stable curves. We restore this…

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of commutative rings that includes the localizations of 1-generated…

In the present paper, we define a notion of numerical equivalence on Chow groups or Grothendieck groups of Noetherian local rings, which is an analogue of that on smooth projective varieties. Under a mild condition, it is proved that the…

The purpose of this article is to prove that Gersten's conjecture for a commutative regular local ring is true. As its applications, we will prove the vanishing conjecture for certain Chow groups, generator conjecture for certain $K$-groups…

We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification…

In this paper, the Lawson homology and morphic cohomology are defined on the Chow motives. We also define the rational coefficient Lawson homology and morphic cohomology of the Chow motives of finite quotient projective varieties. As a…

We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we…

We introduce a natural structure of a semigroup (isomorphic to a factorization semigroup of the unity in the symmetric group) on the set of irreducible components of Hurwitz space of marked degree $d$ coverings of $\mathbb P^1$ of fixed…

Let M of real dimension 2n-1 be a compact, orientable, weakly pseudoconvex manifold of dimension at least five, embedded in C^N (n less than or equal to N), of codimension one or more in C^N, and endowed with the induced CR structure. We…

Our main goal is to give a sense of recent developments in the (stable) rationality problem from the point of view of unramified cohomology and 0-cycles as well as derived categories and semiorthogonal decompositions, and how these…

We apply the machinery of relative tensor triangular Chow groups to the action of the derived category of quasi-coherent sheaves on a noetherian scheme $X$ on the derived category of quasi-coherent $\mathcal{A}$-modules, where $\mathcal{A}$…

The three famous problems concerning units, zero-divisors and idempotents in group rings of torsion-free groups, commonly attributed to I. Kaplansky, have been around for more than 60 years and still remain open in characteristic zero. In…

The description of the subgroup structure of a non-commutative division ring is the subject of the intensive study in the theory of division rings in particular, and of the theory of skew linear groups in general. This study is still so far…

We study the Cohen-Macaulay property of a particular class of radical extensions of an unramified regular local ring having mixed characteristic.

In this paper, we investigate the question of triviality of the rational Chow groups of complete intersections in projective spaces and obtain improved bounds for this triviality to hold. Along the way, we study the dimension and…

We define the logarithmic tautological rings of the moduli spaces of Deligne-Mumford stable curves (together with a set of additive generators lifting the decorated strata classes of the standard tautological rings). While these algebras…