相关论文: Invitation to higher local fields, Part I, section…

This is a presentation of main ingredients of Kato's higher local class field theory.

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

This is an introduction to author's ramification theory of a complete discrete valuation field with residue field whose p-basis consists of at most one element. New lower and upper filtrations are defined; cyclic extensions of degree p may…

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.

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…

Using the higher tame symbol and Kawada and Satake's Witt vector method, A. N. Parshin developed class field theory for higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We extend…

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 work studies two dimensional local skew fields and their automorphisms.

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.

We construct a theory of higher local symbols along Parsin chains for reciprocity sheaves. Applying this formalism to differential forms, gives a new construction of the Parsin-Lomadze residue maps, and applying it to the torsion characters…

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.

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 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…

This work sketches the author classification of complete discrete valuation fields K of characteristic 0 with residue field of characteristic p into two classes depending on the behaviour of the torsion part of a differential module. For…

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…

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…

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…

Ramification theory of monogenic extensions of complete discrete valuation fields is presented. Relations to Kato's conductor are discussed.

This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…

For an arbitrary field p-torsion and cotorsion of the Milnor groups K_n(F) and K_n^{t}(F)=K_n(F)/\cap_{l\ge1} lK_n(F) are discussed. The work contains further discussions of an analogue of Satz 90 for K_n(F) and K_n^{t}(F) and computation…