Related papers: $K$-stable splendid Rickard complexes

We adapt Grayson's model of higher algebraic $K$-theory using binary acyclic complexes to the setting of stable $\infty$-categories. As an application, we prove that the $K$-theory of stable $\infty$-categories preserves infinite products.

Let $H$ be a finite quasisimple classical group, i.e. $H$ is perfect and $S:=H/Z(H)$ is a finite simple classical group. We prove in this paper that, excluding the cases when the simple group $S$ has a very exceptional Schur multiplier such…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…

In this note we define the stabilizer group of any adjoint-invariant $l$-form on a complex simple Lie algebra. This result partially extend a previous result by Kable.

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's…

In the context of holomorphic families of ${\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]

We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersection. Thus, near-cones of sufficiently high depth satisfy…

We prove that finite-dimensional Jacobian algebras associated with non-degenerate quivers with potentials satisfy the stable Brauer-Thrall II' conjecture. In particular, this implies that the brick Brauer-Thrall II' conjecture (also known…

Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…

We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound…

Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical twists. Using this, we give new proofs of the following…

We give a new proof of the following theorem: moduli spaces of stable complexes on a complex projective K3 surface, with primitive Mukai vector and with respect to a generic Bridgeland stability condition, are hyperk\"{a}hler varieties of…

Stembridge introduced the notion of stability for Kronecker triples which generalize Murnaghan's classical stability result for Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triple,…

We extend theorems of Breuillard-Kalantar-Kennedy-Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C*-algebras is stable under taking reduced crossed product over discrete…

Fisher [Fis75] and Baur [Bau75] showed independently in the seventies that if $T$ is a complete first-order theory extending the theory of modules, then the class of models of $T$ with pure embeddings is stable. In [Maz4, 2.12], it is asked…

Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple…

In this short note we provide a relatively simple proof of the Erd\H{o}s-Hajnal conjecture for families of finite (hyper-)graphs without the $k$-order property. It was originally proved by M. Malliaris and S. Shelah in "Regularity lemmas…

A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…