Related papers: Invitation to higher local fields, Part I, section…
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…
Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.
This is a presentation of main ingredients of Kato's higher local class field theory.
Certain topologies on Milnor K-groups of higher local fields K are studied. These are related to the topology on the multiplicative group and important for explicit higher local class field theory. The structure of the quotient of Milnor…
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
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 review of Parshin's higher local class field theory in characteristic p.
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.
In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $\operatorname{GL}_{1}$ defined over $p$-adic fields $K$. We do this by redeveloping the theory of proalgebraic groups and use this…
Koya's and author's approach to the higher local reciprocity map as a generalization of the classical class formations approach to the level of complexes of Galois modules.
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…
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.
An exponential homomorphism for a complete discrete valuation field of characteristic zero which relates differential forms and the Milnor K-groups of the field is studied. An application to explicit formulas is included.
We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in…
This appendix discusses some basic definitions and properties of differential forms and Kato's cohomology groups in characteristic p and a sketch of the proof of Bloch-Kato-Gabber's theorem which describes the differential symbol from the…
This is a concise survey of links between Galois module theory and class field theory (CFT). It explores various uses of CFT in Galois module theory, it comments on the absence of CFT in contexts where it might be expected to play a role…
A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an…
This work studies two dimensional local skew fields and their automorphisms.
We present a general formalism for higher dimensional versions of lattice gauge fields based on higher strict homotopy groupoids. First, using the language of nonabelian Algebraic Topology, we define local lattice higher gauge fields. Then,…
This is a review of the vast area of explicit formulas for the (wild) Hilbert symbol (not only in the one-dimensional case but in the higher dimensional case as well). An extensive bilbiography is included.