#### Geometry & Topology Monographs 3 (2000) -
Invitation to higher local fields,
Part I, section 4, pages 43-51

## Cohomological symbol for henselian discrete valuation fields of
mixed characteristic

### J. Nakamura

**Abstract**.
This is a sketch of main steps of the proof
of Bloch--Kato's theorem which states that
the norm residue homomorphism

K_q(K)/m\to H^q(K,\Bbb Z/m(q))

is an isomorphism for a henselian discrete valuation field K
of characteristic 0 with residue field of positive characteristic.

**Keywords**. Henselian discrete valuation fields, cohomological symbol, Bloch-Kato theorem.

**AMS subject classification**. 19D45, 19D99, 12G05.
**E-print:** `arXiv:math.NT/0012135`

Jinya Nakamura

Department of Mathematics, University of Tokyo

3-8-1 Komaba Meguro-Ku 153-8914 Japan

Email: jinya@ms357.ms.u-tokyo.ac.jp

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