p-Henselian field: K-theory, Galois cohomology, and graded Witt rings

Adrian R. Wadsworth

Vol. 105 (1983), No. 2, 473–496

DOI: 10.2140/pjm.1983.105.473

Abstract

For a field F with a p-Henselian valuation v, direct sum decompositions will be proved for Milnor’s K-theory mod n (n a power of the prime p), for the Galois cohomology of F with Z_n-coefficients, and for the graded Witt ring of quadratic forms of F (with p = 2). In each case, the summands of the ring associated to F are copies of the corresponding ring associated to the residue field of v, and the number of summands is determined by its value group. The theorems generalize results known for a field with a complete discrete valuation.

Mathematical Subject Classification 2000

Primary: 12J10

Secondary: 13J15

Milestones

Received: 8 September 1981

Published: 1 April 1983