Related papers: A freeness criterion for complexes with derived ac…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
Given a separable nonconstant polynomial $f(x)$ with integer coefficients, we consider the set $S$ consisting of the squarefree parts of all the rational values of $f(x)$, and study its behavior modulo primes. Fixing a prime $p$, we…
For the Cousin complex of certain modules, we investigate finiteness of cohomology modules, local duality property and injectivity of its terms. The existence of canonical modules of Noetherian non-local rings and the Cousin complexes of…
We prove that the depth formula holds for $\Tor$-independent modules in certain cases over a Cohen-Macaulay local ring, provided one of the modules has reducible complexity.
We provide new results on the vanishing of local cohomology modules supported at ideals of minors of matrices over arbitrary commutative Noetherian rings. In the process, we compute the local cohomology of rings of polynomials with integer…
We present an Avoidance Principle for certain graded rings. As an application we fill a gap in the proof of a result by Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert-Samuel multiplicity of the graded components of…
An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…
This work concerns finite free complexes with finite length homology over a commutative noetherian local ring $R$. The focus is on complexes that have length $\mathrm{dim}\, R$, which is the smallest possible value, and in particular on…
In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic…
We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse complex. Even…
We present a method to quantize free fermions which eliminates the doublers when implemented on the lattice in any number of dimensions and in the $m=0$ limit. The elimination of doublers is achieved by combining a second-order description…
Let $G$~be a real Lie group and let $G^\circ$ be the identity component of~$G$. Let $G$~act on a $C^\infty$ real manifold~$M$. Assume the action is $C^\infty$. Assume that the fixpoint set of any nontrivial element of~$G^\circ$ has empty…
The generalisation of the well-known (Hilbert polynomial) criterion for flatness of a projective morphism of Noetherian schemes is given for the case of nonreduced base of the morphism.
The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
We define and calculate the weighted multiplicities of non Gorenstein terminal singularities on threefolds and some quotient singularities. We improve freeness conditions on threefolds.
We consider simplicial complexes admitting a free action by an abelian group. Specifically, we establish a refinement of the classic result of Hochster describing the local cohomology modules of the associated Stanley--Reisner ring,…
We study some properties of the varieties of deformations of free groups in compact Lie groups. In particular we prove a conjecture of Margulis and Soifer about the density of non-virtually free points in such variety, and a conjecture of…
We give a negative answer to Problem 19 of Cahen, Fontana, Frisch, and Glaz concerning the flatness and freeness of rings of integer-valued polynomials. We construct an explicit one-dimensional Noetherian local domain D over the field with…
We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a…