Related papers: Global representation theory: Homological foundati…

Let $G=G_1 \times G_2$ be a finite group. We know that the second cohomology group $H^2(G,\mathbb C^\times)$ is isomorphic to $H^2(G_1,\mathbb C^\times) \times H^2(G_2,\mathbb C^\times) \times Hom(G_1/G_1' \otimes_\mathbb Z G_2/G_2',…

Let $U$ be a unipotent group which is graded in the sense that it has an extension $H$ by the multiplicative group of the complex numbers such that all the weights of the adjoint action on the Lie algebra of $U$ are strictly positive. We…

These are expanded notes from some talks given during the fall 2002, about ``homotopical algebraic geometry'' (HAG) with special emphasis on its applications to ``derived algebraic geometry'' (DAG) and ``derived deformation theory''. We use…

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

We give a classification theorem for certain four-dimensional families of geometric $\lambda$-adic Galois representations attached to a pure motive. More precisely, we consider families attached to the cohomology of a smooth projective…

Let $G$ be a reductive $p$-adic group. We prove that all supercuspidal representations of $G$ arise through Yu's construction subject to certain hypotheses on $k$ (depending on $G$). As a corollary, under the same hypotheses, we see that…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

Let $G$ and $T$ be topological groups, $\alpha : T \to \Aut(G)$ a homomorphism defining a continuous action of $T$ on $G$ and $G^\sharp := G \rtimes_\alpha T$ the corresponding semidirect product group. In this paper we address several…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…

Let $W$ be a group endowed with a finite set $S$ of generators. A representation $(V,\rho)$ of $W$ is called a reflection representation of $(W,S)$ if $\rho(s)$ is a (generalized) reflection on $V$ for each generator $s \in S$. In this…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

Let G be a connected reductive algebraic group over a perfect field. We study the representability of the equivariant automorphism group of G-varieties. For a broad class of complexity-one G-varieties, we show that this group is…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global…

This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) deformation functors to an appropriate bicategory of artinian DG…

Motivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of complex dimension $n$ in general position.…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

We study compatible families of four-dimensional Galois representations constructed in the \'{e}tale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain conditions are…

We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…