Related papers: More ghost modules I

We describe torsion classes in the first cohomology group of $\text{SL}_2(\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology…

Exceptional modules are tree modules. A tree module usually has many tree bases and the corresponding coefficient quivers may look quite differently. The aim of this note is to introduce a class of exceptional modules which have a…

We consider the ring of coinvariants for modular representations of cyclic groups of prime order. For all cases for which explicit generators for the ring of invariants are known, we give a reduced Gr\"obner basis for the Hilbert ideal and…

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.

We show that general infrared modifications of the Einstein-Hilbert action obtained by addition of curvature invariants are not viable. These modifications contain either ghosts or light gravity scalars. A very specific fine-tuning might…

It is natural to try to place the new polynomial invariants of links in algebraic topology (e.g. to try to interpret them using homology or homotopy groups). However, one can think that these new polynomial invariants are byproducts of a…

The moduli space of Anosov representations of a surface group in a semisimple group, which is an open set in the character variety, admits many more natural functions than the regular functions. We will study in particular length functions…

We construct new moduli spaces of quiver representations with multiplicities, i.e. over rings of truncated power series. This includes moduli of framed representations and analogues of Nakajima quiver varieties. Our construction relies on…

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three modules give us a new…

This paper generalize the idea of the authors in \cite{Bennis and Mahdou1}. Namely, we define and study a particular case of modules with Gorenstein projective, injective, and flat dimension less or equal than $n\geq 0$, which we call,…

The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…

When one uses the Dirac bracket, second class constraints become first class. Hence, they are amenable to the BRST treatment characteristic of ordinary first class constraints. This observation is the starting point of a recent…

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to…

This is the third part of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present article we construct and study some examples of Drinfeld modular forms. In particular we define…

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically…

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These…

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories…

Modular categories are a well-known source of quantum 3-manifold invariants. In this paper we study structures on modular categories which allow to define refinements of quantum 3-manifold invariants involving cohomology classes or…

In this article, the existence of ghost classes for the Shimura varieties associated to algebraic groups of orthogonal similitudes of signature (2, n) is investigated. We make use of the study of the weights in the mixed Hodge structures…

The formalism of injective stabilization of additive functors is used to define a new notion of the torsion submodule of a module. It applies to arbitrary modules over arbitrary rings. For arbitrary modules over commutative domains it…