Related papers: Towards Vorst's conjecture in positive characteris…

We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.

We identify a positivity property for partition functions in quantum systems with a unitary symmetry group, and we call this "twist positivity." The existence of Feynman-Kac measures and the existence of zero-mass limits are both related to…

We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid, and strongly-rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion…

We prove a conjecture about mininmal index of certain representations of Coset Algebraic Conformal Field Theories under general conditions as formulated previously by us. As a by-product, the Kac-Wakimoto Conjecture (KWC) which is related…

In this note I give a description of Lyubeznik's local cohomology invariants for a certain natural class of local rings, namely the ones which have the same local cohomology vanishing as one expects from an isolated singularity. This…

Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten conjecture, then so is S. In this paper, we consider the…

Let H be a homology theory for algebraic varieties over a field k. To a complete k-variety X, one naturally attaches an ideal of the coefficient ring H(k). We show that, when X is regular, this ideal depends only on the upper Chow motive of…

In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…

We prove a conjecture of Lehmann-Tanimoto about the behaviour of the Fujita invariant (or $a$-constant appearing in Manin's conjecture) under pull-back to generically finite covers. As a consequence we obtain results about geometric…

We investigate conditions under which the endomorphism ring of the Leavitt path algebra $L_{K}(E)$ possesses various ring and module-theoretical properties such as being von Neumann regular, $\pi$-regular, strongly $\pi$-regular or…

The main result of the work ``The nilpotence conjecture in K-theory of toric varieties'' is extended to all coefficient fields of characteristic 0, thus covering the class of genuine toric varieties.

We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable $\infty$-category of non-$\mathbb A^1$-invariant motivic spectra, which turns out to be…

The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded…

This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra $A$ are reflected in the regularities of certain (complexes of) $A$-modules. We study the classical Tor-regularity and…

Let G be a simple complex algebraic group and g its Lie algebra. We show that the g-Witten-Reshetikhin-Turaev quantum invariants determine a deformation-quantization, C_q[X_G(torus)], of the coordinate ring of the G-character variety of the…

For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory,…

One of the many equivalent formulation of the K\"othe's conjecture is the assertion that there exists no ring which contains two nil right ideals whose sum is not nil. We discuss several consequences of an observation that if the Koethe…

This paper is devoted to present some characterizations for a local ring to be generically Gorenstein and Gorenstein by means of $\delta$-invariant and linkage theory.

We prove Fujita's freeness conjecture for Gorenstein complexity-one $T$-varieties with rational singularities.

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself equals to a given element of the ring.