This monograph 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 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 areas (Part II).

The volume grew as an extended version of talks given at the
conference. The two parts are separated by a paper of K. Kato, an
IHES preprint from 1980 which has never been published.

An n-dimensional local field is a complete discrete valuation field
whose residue field is an (n-1)-dimensional local field; 0-dimensional
local fields are just perfect (e.g. finite) fields of positive
characteristic. Given an arithmetic scheme, there is a higher local
field associated to a flag of subschemes on it. One of central
results on higher local fields, class field theory, describes abelian
extensions of an n-dimensional local field via (all in the case of
finite 0-dimensional residue field; some in the case of infinite
0-dimensional residue field) closed subgroups of the n-th Milnor
K-group of F.

We hope that the volume will be a useful
introduction and guide to the subject.
The contributions to this volume were received over the period
November 1999 to August 2000 and the electronic publication date is 10 December 2000.

*Ivan Fesenko and Masato Kurihara*

- Igor Zhukov

2. Pages 19-29 :
**
p-primary part of the Milnor K-groups and Galois cohomology
of fields of characteristic p
**

- Oleg Izhboldin

3. Pages 31-41 :
**
Appendix to Section 2
**

- Masato Kurihara and Ivan Fesenko

4. Pages 43-51 :
**
Cohomological symbol for henselian discrete valuation fields of mixed
characteristic
**

- Jinya Nakamura

5. Pages 53-60 :
**
Kato's higher local class field theory
**

- Masato Kurihara

6. Pages 61-74 :
**
Topological Milnor K-groups of higher local fields
**

- Ivan Fesenko

7. Pages 75-79 :
**
Parshin's higher local class field theory in characteristic p
**

- Ivan Fesenko

8. Pages 81-89 :
**
Explicit formulas for the Hilbert symbol
**

- Sergei V. Vostokov

9. Pages 91-94 :
**
Exponential maps and explicit formulas
**

- Masato Kurihara

10. Pages 95-101 :
**
Explicit higher local class field theory
**

- Ivan Fesenko

11. Pages 103-108 :
**
Generalized class formations and higher class field theory
**

- Michael Spiess

12. Pages 109-112 :
**
Two types of complete discrete valuation fields
**

- Masato Kurihara

13. Pages 113-116 :
**
Abelian extensions of absolutely unramified complete discrete valuation
fields
**

- Masato Kurihara

14. Pages 117-122 :
**
Explicit abelian extensions of complete discrete valuation fields
**

- Igor Zhukov

15. Pages 123-135 :
**
On the structure of the Milnor K-groups of complete discrete valuation fields
**

- Jinya Nakamura

16. Pages 137-142 :
**
Higher class field theory without using K-groups
**

- Ivan Fesenko

17. Pages 143-150 :
**
An approach to higher ramification theory
**

- Igor Zhukov

18. Pages 151-164 :
**
On ramification theory of monogenic extensions
**

- Luca Spriano

- Kazuya Kato

- A.N. Parshin

2. Pages 215-221 :
**
Adelic constructions for direct images of differentials and symbols
**

- Denis Osipov

3. Pages 223-237 :
**
The Bruhat-Tits buildings over higher dimensional local fields
**

- A.N. Parshin

4. Pages 239-253 :
**
Drinfeld modules and local fields of positive characteristic
**

- Ernst-Ulrich Gekeler

5. Pages 255-262 :
**
Harmonic analysis on algebraic groups over
two-dimensional local fields of equal characteristic
**

- Mikhail Kapranov

6. Pages 263-272 :
**
Phi-Gamma-modules and Galois cohomology
**

- Laurent Herr

7. Pages 273-279 :
**
Recovering higher global and local fields from Galois groups -
an algebraic approach
**

- Ido Efrat

8. Pages 281-292 :
**
Higher local skew fields
**

- Alexander Zheglov

9. Pages 293-298 :
**
Local reciprocity cycles
**

- Ivan Fesenko

10. Pages 299-304 :
**
Galois modules and class field theory
**

- Boas Erez

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**