Related papers: On a generalization of affinoid varieties

We apply Schmidt's Subspace Theorem to establish Arithmetic General Theorems for projective varieties over number and function fields. Our first result extends an analogous result of M. Ru and P. Vojta. One aspect to its proof makes use of…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

Many theorems in complex analysis propagate analyticity, such as the Forelli theorem, edge-of-the-wedge theorem and so on. We give a germination theorem which allows for general analytic propagation in complete normed fields. In turn, we…

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…

A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck…

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between…

We present a general vertex operator construction based on the Fock space for an affine Lie algebras of type $A$. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie…

Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…

Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…

By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…

The primary purpose is to introduce and explore projective varieties, $\text{GRASS}_{\bf d}(\Lambda)$, parametrizing the full collection of those modules over a finite dimensional algebra $\Lambda$ which have dimension vector $\bf d$. These…

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

Let $\textbf{U}^+$ be the positive part of the quantum group $\textbf{U}$ associated with a generalized Cartan matrix. In the case of finite type, Lusztig constructed the canonical basis $\textbf{B}$ of $\textbf{U}^+$ via two approaches.…

In classical geometric algebra, there have been several treatments of affine and projective planes based on fields. In this thesis we approach affine and projective planes from a constructive point of view and we base our geometry on local…

A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new…

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…