Related papers: An introduction to higher dimensional local fields…
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…
It is a survey paper on n-dimensional local fields and adeles on n-dimensional schemes.
We give a new approach for the local class field theory of Serre and Hazewinkel. We also discuss two-dimensional local class field theory in this framework.
This is a presentation of explicit methods to construct higher local class field theory by using topological K-groups, explicit symbols and a generalization of Neukirch-Hazewinkel's axiomatic approaches. The existence theorem is discussed…
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use…
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.
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
This work studies two dimensional local skew fields and their automorphisms.
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
Many active mathematical research topics nowadays include the concepts of valued fields and local fields, especially the local field of p-adic numbers Qp and the field of formal Laurent series F((X)). Local fields are a notion situated in…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…