Related papers: The Balmer spectrum and telescope conjecture for i…
We introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group $B$. Telescopes are inspired from the theory of groups acting on rooted…
We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.
This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…
If $A \colon D(A) \subset \mathcal{H} \to \mathcal{H}$ is an unbounded Fredholm operator of index $0$ on a Hilbert space $\mathcal{H}$ with a dense domain $D(A)$, then its spectrum is either discrete or the entire complex plane. This…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated. Let H be…
This paper is concerned with the Laitinen Conjecture. The conjecture predicts an answer to the Smith question which reads as follows. Is it true that for a finite group acting smoothly on a sphere with exactly two fixed points, the tangent…
Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by reflections about affine hyperplanes; most arise as the…
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We…
We present a novel notion of stable objects in a triangulated category. This Postnikov-stability is preserved by equivalences. We show that for the derived category of a projective variety this notion includes the case of semistable…
The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…
The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $\Gamma_N$ and for a given element $\gamma \in \Gamma_N$, we present an algorithm for finding stabilisers…
We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine whether a class is closed under pure subobjects, pure…
We calculate the particle spectrum of the SSM which follows from the assumption that the commonly assumed universal form of the soft supersymmetry --breaking terms is invariant under renormalisation. It is argued that this ``strong''…
We establish a bijection between torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of indecomposable…
We show that the Friedlander-Mazur conjecture holds for the product of an elliptic curve with some smooth projective variety of dimension 3. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As…
We prove that if $R$ is a ring that is object unital and strongly graded by a groupoid $\Gamma$, and if $\Delta$ is a wide subgroupoid of $\Gamma$, then $R/R_\Delta$ is separable if and only if, for each $e \in \Gamma_0$, there exist $f \in…
Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…
An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed-point net of the field net under a…
We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].