Related papers: B(G) for all local and global fields

In these proceedings we summarize previous work where we formalize a general concept of algebraic field theories using operads. After giving a gentle reminder of algebraic quantum field theory, operads and their algebras, we construct field…

A theorem of B. Green states that if A is a Dedekind ring whose fraction field is a local or global field, every normal projective curve over Spec(A) has a finite morphism to P^1_A. We give a different proof of a variant of this result…

We study global sections of Hodge bundles arising from two complementary constructions: a deformation-theoretic construction, which yields global geometric consequences for period maps, and a construction from the matrix representation of…

In this paper, we obtain global function field versions of the results of Schinzel - Postnikova for multiplicative groups, and of Hahn - Cheon for elliptic curves, which is an analog of the former result.

A comprehensive introduction to two-dimensional conformal field theory is given.

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

We develop the theory of nilpotent $G$-spaces and their localisations, for $G$ a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can…

We study the evaluation maps given by elements of the Brauer group of varieties over local fields. We show constancy of the aforementioned maps in several interesting cases.

We generalize some results in Hodge theory to generalized normal crossing varieties.

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…

We consider higher-dimensional analogues of the classical Brauer-Siegel theorem focusing on the case of abelian varieties over global function fields. We prove such an analogue in the case of constant families of elliptic curves and abelian…

A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…

We present a complete suite of algorithms for finding isotropic vectors of quadratic forms (of any dimension) over an arbitrary global field of characteristic different from 2. This is a new version with numerous changes and improvements.

The magnetic backgrounds that physically give rise to spacetime noncommutativity are generally treated using noncommutative geometry. In this article we prove that also the theory of generalised complex manifolds contains the necessary…

Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…

We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.

We establish the Hasse principle (local-global principle) in the context of the Baum-Connes conjecture with coefficients. We illustrate this principle with the discrete group $GL(2,F)$ where $F$ is any global field.

We introduce an equation named matrix Dirac equation which can be considered as a generalization of Dirac equation for an electron. The liaison between matrix Dirac equation and standard Dirac equation is discussed. We write a lagrangian…