Related papers: The deformation theory of local complete intersect…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
Let $(L, \alpha)$ be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notions of generalized derivations and representations of…
The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.
We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various…
We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
We prove the following criterion for the pro-representability of the deformation cohomology of a commutative formal Lie group. Let f be a flat and separated morphism between noetherian schemes. Assume that the target of f is flat over the…
A construction of the tangent dg Lie algebra of a sheaf of operad algebras on a site is presented. The requirements on the site are very mild; the requirements on the algebra are more substantial. A few applications including the…
We construct a tangent-obstruction theory for Azumaya algebras equipped with a quadratic pair. Under the assumption that either 2 is a global unit or the algebra is of degree 2, we show how the deformation theory of these objects reduces to…
This paper is devoted to deformation theory of graded Lie algebras over $\Z$ or $\Z_l$ with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger…
This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\Def ^{\h}(E)$,…
This paper contributes to the theory of singularities of meromorphic linear ODEs in traceless $2\times2$ cases, focusing on their deformations and confluences. It is divided into two parts: The first part addresses individual singularities…
The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to…
The purpose of this expository paper is to explain how the Fargues-Fontaine curve and its decomposition into a punctured curve and the formal neighborhood of the puncture naturally arise from various forms of topological cyclic homology and…
We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we…
An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…
This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…