Related papers: Invitation to higher local fields, Part I, section…
Theory for open curves over a local field. After introducing the reciprocity map, we determine the kernel and the cokernel of this map. In addition to this, the Pontrjagin dual of the reciprocity map is also investigated. This gives the one…
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…
The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.
In this note we introduce higher order polar loci as natural generalizations of the classical polar loci, replacing the role of tangent spaces by that of higher order osculating spaces. The close connection between polar loci and dual…
This work contains a list of all known results on the quotient filtration on the Milnor K-groups of a complete discrete valuation field in terms of differential modules over the residue field . Author's recent study of the case of a tamely…
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules…
Viewing higher local fields as ring objects in the category of iterated pro-ind-objects, a definition of open subgroups in Milnor K-groups of the fields is given. The self-duality of the additive group of a higher local field is proved. By…
Let $V$ be a projective limit, with respect to the renormalized norm mappings, of the groups of principal units corresponding to a strictly increasing sequence of finite separable totally and tamely ramified Galois extensions of a local…
In our previous paper we describe the Galois module structures of $p$th-power class groups $K^\times/{K^{\times p}}$, where $K/F$ is a cyclic extension of degree $p$ over a field $F$ containing a primitive $p$th root of unity. Our…
In this paper, we consider infinite Galois extensions of number fields and study the relation between their local degrees and the structure of their Galois groups. It is known that, if $K$ is a number field and $L/K$ is an infinite Galois…
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…
This work studies two dimensional local skew fields and their automorphisms.
We discuss some properties of the tower of mapping class group representations associated to a Rational Conformal Field Theory. In particular, after reviewing the elementary properties of the modular representation, we discuss the Galois…
We investigate the class field theory for products of open curves over a local field. In particular, we determine the kernel of the reciprocity homomorphism.
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete…
We study a dynamical system induced by the Artin reciprocity map for a global field. We translate the conjugacy of such dynamical systems into various arithmetical properties that are equivalent to field isomorphism, relating it to…
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.
Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…
Several questions about the Galois group of field generated by certain one dimensional formal group laws are studied. This is continuation of author's prior article titled 'Field Generated by Division Points of Certain Formal Group Laws -…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…