Related papers: Notes on identical configurations in Abelian Sandp…
We give a presentation of abelian class field theory.
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
We analyze flat S_3-covers, attempting to create structures parallel to those found in the abelian theory. We use an initial local analysis as a guide in finding a global description.
Let X/k be an abelian variety over an algebraically closed field k of characteristic p > 0. In this paper, using the Azumaya property of the sheaf of crystalline differential operators and the Morita equivalence, we show that etale locally…
This paper presents a study of the LLL algorithm from the perspective of statistical physics. Based on our experimental and theoretical results, we suggest that interpreting LLL as a sandpile model may help understand much of its mysterious…
The aim of this paper is to study a conjecture predicting a lower bound on the canonical height on abelian varieties, formulated by S. Lang and generalized by J. H. Silverman. We give here an asymptotic result on the height of Heegner…
We introduce and study the notion of \emph{semiadditive height} for higher semiadditive $\infty$-categories, which generalizes the chromatic height. We show that the higher semiadditive structure trivializes above the height and prove a…
Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We put ASMs into a larger context by studying the order ideals of subposets of a…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d >= 3, we show that this problem is P-complete, so that explicit simulation of the system is…
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
This is a note constructing a certain weight 4 automorphic form on the moduli space of cubic surfaces, posted here because it is referred to in math.AG/0002066
In this paper, firstly, we mainly study the relationship of balanced pairs among three Abelian categories in a recollement. As an application of admissible balanced pairs, we introduce the notion of the relative tilting modules, and give a…
The aim of this note is to discuss resolution theorems that are useful in the study of semi log canonical varieties.
We apply a framework for the description of random tilings without height representation, which was proposed recently, to the special case of quasicrystalline random tilings. Several important examples are discussed, thereby demonstrating…
The purpose of this short paper is to put recent results on the symmetry of the joint distribution of the numbers of crossings and nestings of two edges over matchings, set partitions and linked partitions, in the larger context of the…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…
On an abelian scheme over a smooth curve over $\overline{\mathbb Q}$ a symmetric relatively ample line bundle defines a fiberwise N\'eon-Tate height. If the base curve is inside a projective space, we also have a height on its…