Related papers: Annihilators of Koszul Homologies and Almost Compl…

This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part I, we formulate and motivate three stability problems: 1.…

We show the existence of a self-similar solution for a modified Boltzmann equation describing probabilistic ballistic annihilation. Such a model describes a system of hard-spheres such that, whenever two particles meet, they either…

We introduce the notion of quasi-triviality of quandles and define homology of quasi-trivial quandles. Quandle cocycle invariants are invariant under link-homotopy if they are associated with 2-cocycles of quasi-trivial quandles. We thus…

We give a new proof of a result of Lazarev, that the dual of the circle $S^1_+$ in the category of spectra is equivalent to a strictly square-zero extension as an associative ring spectrum. As an application, we calculate the topological…

We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci…

We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these versions of Koszulity hold for all finitely generated maximal…

Let R be a locally finitely generated algebra over a discrete valuation ring V of mixed characteristic. For any of the homological properties, the Direct Summand Theorem, the Monomial Theorem, the Improved New Intersection Theorem, the…

We completely revised the paper after the referee's comments. In the new version, we replaced two erroneous examples, studied a link with earlier work of Koh and Stilmann, and strengthened the main theorem.

We study the periodic cyclic homology groups of the cross-product of a finite type algebra $A$ by a discrete group $\Gamma$. In case $A$ is commutative and $\Gamma$ is finite, our results are complete and given in terms of the singular…

The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally…

We prove that the automorphism group of a general complete intersection $X$ in a projective space is trivial with a few well-understood exceptions. We also prove that the automorphism group of a complete intersection $X$ acts on the…

Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring, and suppose $R$ is Cohen-Macaulay with canonical module $\omega_R$. We develop new tools for analyzing questions involving annihilators of several homologically defined objects.…

In this paper we show that if $\Lambda=\amalg_{i\geq 0}\Lambda_i$ is a Koszul algebra with $\Lambda_0$ isomorphic to a product of copies of a field, then the minimal projective resolution of $\Lambda_0$ as a right $\Lambda$-module provides…

Thanks to recent results on ring homomorphisms of Azumaya algebras and to the following ones about endomorphisms of canonical Poisson algebras and Dirac quantum algebras, and about the reformulation in positive characteristic of these…

In this paper we examine certain filtrations of topological Hochschild homology and topological cyclic homology. As an example we show how the filtration with respect to a nilpotent ideal gives rise to an analog of a theorem of Goodwillie…

The Bitableax correspondence isomorphism/Koszul map Theorem (BCK Theorem, for short, Theorem 6.5 below) describes a relevant pair of mutually inverse vector space isomorphisms, the Koszul map K : U(gl(n))-> Sym(gl(n)) and the bitableaux…

In this paper we investigate the monomial ideals which satisfy the copersistence property or nearly copersistence property.

Two ideals $I$ and $J$ are called transverse if $I \cap J = IJ$. We show that the obstructions defined by Avramov for classes of (sequentially) transverse ideals in regular local rings are always $0$. In particular, we compute an explicit…

Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…

Algebras defined over fields of characteristic zero and positive characteristic usually do not behave the same way. However, for certain algebras, for example the group algebras, they behave the same way as the characteristic zero case at…