相关论文: Notes sur la droite projective de Berkovich

It is surprising, but an established fact that the field of Elementary Geometry referring to normed spaces (= Minkowski spaces) is not a systematically developed discipline. There are many natural notions and problems of elementary and…

The Polynomial Freiman-Ruzsa conjecture is one of the central open problems in additive combinatorics. If true, it would give tight quantitative bounds relating combinatorial and algebraic notions of approximate subgroups. In this note, we…

In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products properties of pure-projective modules or pure-injective…

The purpose of this book is to give an exposition of geometry, from a point of view which complements Klein's Erlangen program. The emphasis is on extending the classical Euclidean geometry to the finite case, but it goes beyond that. After…

This paper concerns the \textbf{abstract geometry of numbers}: namely the pursuit of certain aspects of geometry of numbers over a suitable class of normed domains. (The standard geometry of numbers is then viewed as geometry of numbers…

Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime--from a General-Relativistic point of view. But this does not mean that it is…

A two-dimensional Besicovitch set over a finite field is a subset of the finite plane containing a line in each direction. In this paper, we conjecture a sharp lower bound for the size of such a subset and prove some results toward this…

Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…

In this note we construct exact solution of Berkovits'superstring field theory.

A projective link is a smooth closed 1-submanifold of the real projective space of dimension three. A projective link is said to be affine if it is isotopic to a link, which does not intersect some projective plane. The main result: a…

This is an overview of the method of pure spinor superfields, written for "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I. Shapiro. The main focus is on the use of the formalism in maximal supergravity on a flat background.…

We study the Das-Jevicki collective field description of arbitrary classical solutions in the c=1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2d string theory. Our analysis naturally includes the case of…

Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the…

In this article, we carry out the flattening techniques developped in a former work in order to ``embellish" a map between compact analytic spaces, to describe the structure of its image, getting this way a substitute for Chevalley's…

With the concept of "discrete space-time" the space-time continuum is resolved into discrete points at the scale of the Planck length. We postulate with the "principle of the fermionic projector" that physical equations must be formulated…

Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi…

This paper presents a complete classification of left-invariant affine and projective vector fields on five-dimensional simply connected nilpotent Lie groups endowed with Riemannian metrics. Building on the classification of left-invariant…

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry canbe used to compactify buildings. We…

The aim of this short note is to give a simple proof of the non-rationality of the double cover of the three-dimensional projective space branched over a sufficiently general quartic.