Related papers: Derived invariance of Hochschild-Mitchell (co)homo…

Since 2005 a new powerful invariant of an algebra emerged using earlier work of Horv\'ath, H\'ethelyi, K\"ulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the centre of a finite dimensional algebra over…

In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is one-to-one correspondence between…

We show that an important classical fixed point invariant, the Reidemeister trace, arises as a topological Hochschild homology transfer. This generalizes a corresponding classical result for the Euler characteristic and is a first step in…

In order to study the Hochschild cohomology of triangular algebras $\mathcal T$, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with $\mathcal T$, and which…

In this paper, we introduce a notion of derived involutive algebras in $ C_2 $-Mackey functors which simultaneously generalize commutative rings with involution and the (non-equivariant) derived algebras of Bhatt--Mathew and Raksit. We show…

We give an interpretation of the Brauer group of a purely inseparable extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted Lie-Rinehart…

The paper is devoted to study some of the questions arises naturally in connection to the notion of relative derived categories. In particular, we study invariants of recollements involving relative derived categories, generalise two…

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…

We provide a factorization model for the continuous internal Hom, in the homotopy category of $k$-linear dg-categories, between dg-categories of equivariant factorizations. This motivates a notion, similar to that of Kuznetsov, which we…

We consider invariant covariant derivatives on reductive homogeneous spaces corresponding to the well-known invariant affine connections. These invariant covariant derivatives are expressed in terms of horizontally lifted vector fields on…

We describe extension classes arising in the $\ell$-adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that this description is consistent with the "plectic conjectures"…

We study twisted derived equivalences of hyper-K\"ahler fourfolds. We describe when two hyper-K\"ahler fourfolds of $K3^{[2]}$-type of Picard rank $1$ with isomorphic transcendental lattices are derived equivalent. Then we present new…

We prove a version of J.P. May's theorem on the additivity of traces, in symmetric monoidal stable $\infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an…

In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a…

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.

A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…

In this short paper we prove a derived version of the Riemann-Hilbert correspondence of Deligne and Simpson. Our generalization is twofold: on one side we consider families of representations of the full homotopy type of a smooth analytic…

Let $X$ be a smooth proper variety over a field $k$ and suppose that the degree map $\mathrm{CH}_0(X \otimes_k K) \to \mathbb{Z}$ is isomorphic for any field extension $K/k$. We show that $G(\mathrm{Spec} k) \to G(X)$ is an isomorphism for…

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this…

In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a…