Related papers: Spherical Twists for Gorenstein Orders and $G$-Hil…

We study two-dimensional $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on the $\Omega$-deformed sphere, $S^2_\Omega$, which is a one-parameter deformation of the $A$-twisted sphere. We provide an exact formula for the…

For every adjunction of stable $\infty$-categories -- or more generally, in any locally stable $(\infty,2)$-category -- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence,…

We study derived categories of Gorenstein varieties X and X^+ connected by a flop. We assume that the flopping contractions f: X \to Y, f^+: X^+ \to Y have fibers of dimension bounded by 1 and Y has canonical hypersurface singularities of…

We show that for every smooth projective surface X and every $n\ge 2$ the push-forward along the diagonal embedding gives a $P^{n-1}$-functor into the $S_n$-equivariant derived category of X^n. Using the Bridgeland--King--Reid--Haiman…

We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…

A higher order theory of gravitation is considered which is obtained by modifying Einstein field equations. The Lagrange used to modify this in the form a polynomial in (scalar curvature) R. In this equation we have studied spherical…

We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and…

We study triangulated categories which can be modeled by an oriented marked surface $\mathcal{S}$ and a line field $\eta$ on $\mathcal{S}$. This includes bounded derived categories of gentle algebras and -- conjecturally -- all partially…

We prove that the Nakayama automorphism of a Frobenius algebra acts trivially on the Hochschild cohomology of the algebra. As an application of this fact, we show how to construct certain invariants attached to such algebras, and to their…

Let $\k$ be a commutative ring, and let $(A,\mfrak{a})$ be an adic ring which is a $\k$-algebra. We study complete and torsion versions of the derived Hochschild homology and cohomology functors of $A$ over $\k$. To do this, we first…

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded…

Given any Koszul algebra of finite global dimension one can define a new algebra, which we call a higher zigzag algebra, as a twisted trivial extension of the Koszul dual of our original algebra. If our original algebra is the path algebra…

Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and…

We investigate deformations of the shuffl e Hopf algebra structure Sh(A) which can be de fined on the tensor algebra over a commutative algebra A. Such deformations, leading for example to the quasi-shuffl e algebra QSh(A), can be…

We calculate explicit formulas for the general equivariant Bondal-Orlov functors on the localized K-theory groups for a crepant birational transformation of toric DM stacks. We recall some facts that the Bondal-Orlov functors give…

In this paper, we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras. We show that the notion of local cohomology functor can be used to detect the Gorensteinness of a homologically smooth…

We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups…

We introduce a cotwist construction for Hopf algebroids that also entails cotwisting or `quantisation' of the base and which is dual to a previous twisting construction of P. Xu. Whereas the latter applied the construction to the algebra of…

We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and $\mathcal{N}=2$ or $\mathcal{N}=4$ supersymmetry, described in $\mathcal{N}=2$ superspace in terms of nonlinear chiral multiplets. We…

We introduce twisted Steinberg algebras over a commutative unital ring $R$. These generalise Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C*-algebras. In particular, for each ample Hausdorff groupoid…