Related papers: Local Borcherds Products for Unitary Groups

We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and use them to describe both the definable and classical Bohr…

We compute the Poisson boundary of locally discrete groups of diffeomorphisms of the circle.

The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures…

We use our extension of the Noether-Lefschetz theorem to describe generators of the class groups at the local rings of singularities of very general hypersurfaces containing a fixed base locus. We give several applications, including (1)…

We show that every Fricke invariant meromorphic modular form for $\Gamma_0(N)$ whose divisor on $X_0(N)$ is defined over $\mathbb{Q}$ and supported on Heegner divisors and the cusps is a generalized Borcherds product associated to a…

Structural properties of unitary groups over local, not necessarily commutative, rings are developed, with applications to the computation of the orders of these groups (when finite) and to the degrees of the irreducible constituents of the…

We develop an obstruction theory for the existence and uniqueness of a solution to the gluing problem for a destriction functor and apply it to some well-known biset functors. The obstruction groups for this theory are reduced cohomology…

We derive a local index theorem in Quillen's form for families of Cauchy-Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces) that are quotients of the hyperbolic plane by the action of cofinite finitely generated…

We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In…

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…

We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of…

In this note we introduce the concept of reflective projective varieties. These are stratified projective varieties with certain dimension constraints on their dual varieties. We prove that for such varieties, the Chern-Schwartz-MacPherson…

In this paper, we introduce restricted products for families of locally convex spaces and formulate criteria ensuring that mappings into such products are continuous or smooth. As a special case, can define restricted products of weighted…

We extend several results of Helfer, Wise, Louder and Wilton related to coherence in one-relator groups to the more general setting of one-relator products of locally indicable groups. The methods developed to do so also give rise to a new…

Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or hereditary torsion pairs) in various derived categories of…

The present exploratory paper deals with tensor products in the locality framework {developed in previous work}, a natural setting for an algebraic formulation of the locality principle in quantum field theory. Locality tensor products of…

The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…

In this short note we show that representation and character varieties of discrete groups can be viewed as tensor products of suitable functors over the PROP of cocommutative Hopf algebras. Such view point has several interesting…

In the present paper we find explicit formulas for the degrees of Heegner divisors on arithmetic quotients of the orthogonal group $\Orth(2,p)$ and for the integrals of certain automorphic Green's functions associated with Heegner divisors.…

We define a tensor product of linear sites, and a resulting tensor product of Grothendieck categories based upon their representations as categories of linear sheaves. We show that our tensor product is a special case of the tensor product…