相关论文: Non-adic formal schemes

We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces together with an additional uniform…

This survey article concerns inducing schemes in the context of interval maps. We explain how the study of these induced systems allows for the fine description of, not only, the thermodynamic formalism for certain multimodal maps, but also…

An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studying due to various connections with representation theory and…

The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…

In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…

A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…

This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

We set up a framework for using algebraic geometry to study the generalised cohomology rings that occur in algebraic topology. This idea was probably first introduced by Quillen and it underlies much of our understanding of complex oriented…

This a first step to develop a theory of smooth, etale and unramified morphisms between noetherian formal schemes. Our main tool is the complete module of differentials, that is a coherent sheaf whenever the map of formal schemes is of…

This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…

We investigate flat maps where the source or target is a Noetherian ring, giving necessary and/or sufficient conditions on a ring for such maps to exist. Along the way, we develop some general facts about flat ring maps, and exhibit many…

Hypercomputational formal theories will, clearly, be both structurally and foundationally different from the formal theories underpinning computational theories. However, many of the maps that might guide us into this strange realm have…

We construct examples of non-schematic algebraic spaces that become schemes after finite ground field extensions.

We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…

There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…

The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We show arithmetic…

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…