1 edition of **Invitation to higher local fields** found in the catalog.

Invitation to higher local fields

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- 7 Currently reading

Published
**2000** by Geometry and Topology, International Press in Coventry, Somerville, Mass .

Written in English

- Local fields (Algebra) -- Congresses.,
- Class field theory -- Congresses.

**Edition Notes**

Statement | editors, I. Fesenko and M. Kurihara. |

Genre | Congresses. |

Series | Geometry & topology monographs -- vol.3 |

Contributions | Fesenko, I. B., Kurihara, M. |

The Physical Object | |
---|---|

Pagination | xi, 304p. : |

Number of Pages | 304 |

ID Numbers | |

Open Library | OL22026527M |

Denote by Kur the maximal unramified extension of K. In this theory a homomorphism is constructed from the p -part of the group of characters of K to Witt vectors over its residue field. Kato independently about twenty five years ago. Subsection 1. On the structure of the Milnor K -groups of complete discrete valuation fields J.

This is described in Kontsevich's course on deformation theory. Fesenko and F. One of the first ideas in higher class field theory is to work with the Milnor K -groups instead of the multiplicative group in the classical theory. Symbolic Logic,83—

Zhukov Additive Galois modules in discrete valuation fields Algebra i Analiz, vol 9, issue 4,pages Russian translation St. Since its construction, one of the important themes of number theory was its generalizations to other classes of fields or to non-abelian extensions. Weibel, available on Weibel's page. Section 2, written by D. A cone of cone-angle is a metric space that can be formed, if

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Higher local skew fields A.

Section 13, written by M. Section 9, written by M. Theorem Vostokov, Bondarko. Section 10, written by B. The first part presents the theory of higher local fields, very often in the more general setting of complete discrete valuation fields. Garibaldi, Z.

Efrat, introduces recent advances in the zero-dimensional anabelian geometry, that is a characterization of fields by means of their absolute Galois group for finitely generated fields and for higher local fields.

Google Scholar [9] C. If the skew field has one-dimensional residue field which is in its centre, then one is naturally led to the study of automorphisms of the residue field which are associated to a local parameter of the skew field.

Osipov, is a review of his recent work on adelic constructions of direct images of differentials and symbols in the two-dimensional case in the relative situation. Faddeev, St. Higher local skew fields A. For an introduction into several global aspects of the theory see W.

Google Scholar [5] Invitation to higher local fields book. The derived category of finite-dimensional representations of a quiver is an important and somewhat unusual example of a smooth proper DG category.

However, all the valuations obtained this way are in the same class of equivalent valuations. Van den Bergh, Generators and representability of functors in commutative and noncommutative geometry.

However, in this volume mostly the higher local fields over finite fields are considered. Similar Items.

Robinson, One-dimensional fibers of rigid subanalytic sets, J. Then K is a complete discrete valuation field with residue field kF t.

Zhukov Proof. In particular, we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef, Loeser, and Cluckers. Surveys [S4] Adelic approach to the zeta function of arithmetic schemes in dimension two, Moscow Math.

The aim of this book is to provide an introduction to higher local fields and render the main ideas of this theory. Obschestva, vol 2, Russian translation Amer. We hope that this volume, as the first collection of main strands of higher local field theory, will be useful as an introduction and guide on the subject.

To specify the exact meaning of the word, K can be referred to as an n -dimensional local field over a finite resp. Higher dimensional local fields Igor Zhukov We give here basic definitions related to n -dimensional local fields.

Theorem Noether, Deuring. Generalized class formations and higher class field theory M. Kato independently about twenty five years ago. Denote by Kur the maximal unramified extension of K.Abstract: 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, The aim is to provide an introduction to higher local fields (more generally complete discrete valuation fields with arbitrary residue field) and render the main ideas of this theory (Part I), as well as to discuss several applications and connections to other Author: Ivan Fesenko, Masato Kurihara.

Invitation to higher local fields, Part II, section 5: Harmonic analysis on algebraic groups over two-dimensional local fields of equal characteristic Kapranov, Mikhail; Abstract.

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. Cited by: 1. 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 as well. Sep 18, · For a higher local field the previous result and higher local class field theory imply certain restrictions on types of cyclic extensions of the field of sufficiently large degree.

[B12] Explicit higher local class ﬁeld theory, in Invitation to higher local fields, I. Fesenko, M. Kurihara (eds.),Geometry and Topology Monographs, Warwickpp. [B11] Higher class ﬁeld theory without using K-groups, in Invitation to higher local fields, I.

Fesenko, M. Kurihara (eds.), Geometry and Topology Monographs. 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 have non-integer ramification breaks.