Related papers: The Zigzag Hochschild Complex

We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex $\Xi$. In the "flip theory," cells of $\Xi_\mathrm{flip}$ correspond to polygonal…

We define the secondary Hochschild complex for an entwining structure over a commutative $k$-algebra $B$. We show that this complex carries the structure of a weak comp algebra. We obtain two distinct cup product structures for the…

Let G be a connected split reductive group over a complete discrete valuation ring of mixed characteristic. We use the theory of intermediate extensions due to Abe-Caro and arithmetic Beilinson-Bernstein localization to classify irreducible…

We show that there is an almost complex structure on a differential calculus on finite points coming from a bidirected finite graph without multiple edges or loops. We concentrate on a polygon as a concrete case. In particular, a…

In that paper, we recall the notion of the multidegree for $D$-modules, as exposed in a previous paper, with a slight simplification. A particular emphasis is given on hypergeometric systems, used to provide interesting and computable…

The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown…

We describe an $A_\infty$-quasi-equivalence of dg-categories between the first authors' $\mathcal{P}_{\mathcal{A}}$ ---the category of category of prefect $A^0$-modules with flat $\Z$-connection, corresponding to the de Rham dga…

In a previous paper, the first and third authors gave an explicit realization of the geometric Langlands correspondence for hypergeometric sheaves, considered as $\textrm{GL}_n$-local systems. Certain hypergeometric local systems admit a…

In this paper, we will describe a combinatorial object to list the orbits in the ${\mathbb Z}$-graded Lie algebra, their Jordan bloc decomposition, their dimension, their dimension, the partial order and the equivariant local system (up to…

We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute…

Given a zero-dimensional Gorenstein algebra $\mathbb{B}$ and two syzygies between two elements $f_1,f_2\in\mathbb{B}$, one constructs a double complex of $\mathbb{B}$-modules, ${\cal G}_\mathbb{B},$ called the small Gobelin. We describe an…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…

The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.

We construct one parameter families of overconvergent Siegel-Hilbert modular forms. In particular, for any classical Siegel-Hilbert modular eigenform one can find a rigid analytic disc centered at this point, on which an infinite family of…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent…