Related papers: Orthogonal to principal ideles

We define an analog in characteristic $p>0$ of the proalgebraic completion of the topological fundamental group of a complex manifold.

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…

We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.

The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth…

The universal Gr\"obner basis of an ideal is a Gr\"obner basis with respect to all term orders simultaneously. The aim of this paper is to present an algorithmic approach to compute the universal Gr\"obner basis for the toric ideal…

In this article, we construct a generating set of rational invariants for the action of the orthogonal group $\text{O}(n)$ on the space $\mathbb{R}[x_1,\dots,x_n]_{2d}$ of real homogeneous polynomials of even degree $2d$. This generalizes a…

A classic result of Brooks, Smith, Stone and Tutte associates to any finite planar network with distinguished source and sink vertices, a tiling of a rectangle by smaller subrectangles whose aspect ratios are given by the conductances of…

There is a natural generalization of domino tilings to tilings of a polygon by hexagons, or, dually, configurations of oriented curves that meet in triples. We show exactly when two such tilings can be connected by a series of moves…

For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-partitions. To any poset ideal ${\mathcal J}$ in $\text{Hom}(P,\mathbb{N})$, finite or infinite, we associate monomial ideals: the…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

We initiate the study of subgroups $H$ of the general linear group $GL_{\binom{n}{m}}(R)$ over a commutative ring $R$ that contain the $m$-th exterior power of an elementary group $\bigwedge^mE_n(R)$. Each such group $H$ corresponds to a…

For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space.…

Taking into account the correspondence between open groupoids and their quantales, we establish a bijective correspondence between the principal $G$-bundles whose left projection is an open surjection and the principal $\opens(G)$-locales…

The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an…

We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

In this note, we show that, in the setting of Galois pairs, the spherical characters of unitary supercuspidal representations satisfy an orthogonality relation.

For any finite group G, there are several well-established definitions of a G-equivariant spectrum. In this paper, we develop the definition of a global orthogonal spectrum. Loosely speaking, this is a coherent choice of orthogonal…

We extend the definition of the unramified curve-tame cohomology groups to $\mathbb{A}^1$-invariant \'etale sheaves under some additional hypotheses. We define a pairing of this group with the Suslin homology satisfying desirable properties…

We study for rationally connected varieties $X$ the group of degree 2 integral homology classes on $X$ modulo those which are algebraic. We show that the Tate conjecture for divisor classes on surfaces defined over finite fields implies…