Related papers: n-dimensional local fields and adeles on n-dimensi…

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…

This is a survey article on distance-squared mappings and related topics.

This work studies two dimensional local skew fields and their automorphisms.

This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.

We survey algorithms and bounds for constructing planar drawings of graphs in small area.

Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.

We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…

This is a survey paper on Alegbraic Geometry over Lie Algebras

This paper is a survey paper on old and recent results on direction problems in finite dimensional affine spaces over a finite field.

This is a comprehensive study of the relations between the global, local and pointwise variants of irreducibility and integrity of schemes, including examples and counterexamples, and aimed especially at learners of algebraic geometry.

This is a survey paper on the geometrization of the local Langlands correspondence by Fargues-Scholze.

In this paper certain $n$-dimensional inequalities are shown to be equivalent to the inequalities in the one-dimensional setting. By this means, embeddings between weighted local Morrey-type spaces are characterized for some ranges of…

This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.

This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…

In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

We give a brief survey on local holomorphic dynamics in higher dimensions. The main novelty of this note is that we will organize the material by the "level" of local invariants rather than the type of maps.

In this note, we establish a duality result under the residue paring between certain two-dimensional adelic spaces, which are associated to a closed point on an arithmetic surface.

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.