Related papers: Dualizable abelian fibrations
We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…
In this short note, we will explain that the good moduli space morphisms behave as if they are proper when we consider sheaf operations, though they are not separated. For example, the decomposition theorem and the base change theorem hold…
We formulate a division problem for a class of overdetermined systems introduced by L. H{\"o}rmander, and establish an effective divisibility criterion. In addition, we prove a coherence theorem which extends Nadel's coherence theorem from…
We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our…
The Langlands functoriality conjecture envisaged in the bisemialgebra framework is proved to correspond to the nonorthogonal completely reducible cuspidal representations of the bilinear algebraic semigroups.
In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…
This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…
An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's $\times_{A}$-bialgebras is explicitly proven. A new class of examples of bialgebroids is constructed. A (formal) dual of a bialgebroid, termed…
The aim of this paper is to study the cohomology theory of Reynolds Lie algebras equipped with derivations and to explore related applications. We begin by introducing the concept of Reynolds LieDer pairs. Subsequently, we construct the…
The main purpose of this survey is to gather results on the boundedness of the Bergman projection. First, we shall go over some equivalent norms on weighted Bergman spaces $A^p_\omega$ which are useful in the study of this question. In…
In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA,…
We define a sheaf of abelian groups whose cohomology is represented by the cotangent complex. We show how obstructions to some standard deformation problems arise as the classes of torsors under and gerbes banded by this sheaf.
In this paper we define a new cohomology theory for a $B$-algebra $A$. We use this cohomology to study deformations of algebras $A[[t]]$, that have a $B$-algebra structure.
We prove a theorem of splitting for the nonabelian tensor product $L \otimes N$ of a pair $(L,N)$ of Lie algebras $L$ and $N$ in terms of its diagonal ideal $L \square N$ and of the nonabelian exterior product $L \wedge N$. A similar…
A recent attempt to extend the geometric Langlands duality to affine Kac-Moody groups, has led Braverman and Finkelberg [arXiv:0711.2083] to conjecture a mathematical relation between the intersection cohomology of the moduli space of…
We introduce a certain differential graded bialgebra, neither commutative nor cocommutative, that governs perturbations of a differential on complexes supplied with an abstract Hodge decomposition. This leads to a conceptual treatment of…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
This paper is a continuation of a previous paper joint with Dennis Sullivan (arXiv:1704.04308). Working in the context of commutative differential graded algebras, we study the ideal of the cohomology classes which can be annihilated by…