Related papers: Non-adic formal schemes
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…
The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how…
We propose a tool-supported methodology for design-space exploration for embedded systems. It provides means to define high-level models of applications and multi-processor architectures and evaluate the performance of different deployment…
We extend a newly developed formal system for the description of astrophysical maps. In this formalism, we consider the difference between maps to be the distance between elements of a pseudometric space (the space of all such maps). This…
Less explored than their metric (Riemannian) counterparts, metric-affine (or Palatini) theories bring an unexpected phenomenology for gravitational physics beyond General Relativity. Lessons of crystalline structures, where the presence of…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
This paper presents our ongoing work on spatio-temporal models for formal analysis and property-based testing. Our proposed framework aims at reducing the impedance mismatch between formal methods and practitioners. We introduce a set of…
Probably building non procedural languages is the most prospective way for parallel programming just because non procedural means no fixed way for execution. The article consists of 3 parts. In first part we consider formal systems for…
We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We use A_{infinity}-formalism to study variation of cohomology spaces under formal deformations of coherent sheaves on projective varieties. As an application we describe formal neighborhoods of twisted Brill-Noether loci at some points.…
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
We prove a non-integrability result concerning iterative derivations on projective line, where the iterative rule is given by a non-algebraic formal group.
Autonomous systems are highly complex and present unique challenges for the application of formal methods. Autonomous systems act without human intervention, and are often embedded in a robotic system, so that they can interact with the…
The first goal of this article is to survey recent progress in Brill--Noether theory, including both the study of the moduli space of maps from a curve to projective space and the geometry of the resulting curves in projective space. The…
We develop the theory of motivic integration for formal schemes
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
Refinement based formal methods allow the modelling of systems through incremental steps via abstraction. Discovering the right levels of abstraction, formulating correct and meaningful invariants, and analysing faulty models are some of…
We develop a general obstruction theory to the formality of algebraic structures over any commutative ground ring. It relies on the construction of Kaledin obstruction classes that faithfully detect the formality of differential graded…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.