By Barros M.

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Res cor (ii) shq (K) −→ shq (L)G −→ shq (K) is exact. Proof. A nontrivial calculation with symbols, for more details see ([ BK, Prop. 4 ]. Lemma 2. Let K and L be as above. The following conditions are equivalent: res cor (i) hq−1 (K) −→ hq−1 (L)G −→ hq−1 (K) is exact. ∪b res (ii) hq−1 (K) −→ hq (K) −→ hq (L) is exact. Geometry & Topology Monographs, Volume 3 (2000) – Invitation to higher local fields Part I. Section 4. Cohomological symbol for henselian discrete valuation field 49 Proof. This is a property of the cup product of Galois cohomologies for L/K .

Math. 66(1982), 493–510. group of K 2 (F ) , preprint, [MS1] A. S. Merkur’ev and A. A. Suslin, K -cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46(1982); English translation in Math. USSR Izv. 21(1983), 307–340. Geometry & Topology Monographs, Volume 3 (2000) – Invitation to higher local fields Part I. Section 2. K -groups and Galois cohomologies of fields of characteristic p 29 [MS2] A. S. Merkur’ev and A. A. Suslin, The norm residue homomorphism of degree three, Izv.

A nontrivial calculation with symbols, for more details see ([ BK, Prop. 4 ]. Lemma 2. Let K and L be as above. The following conditions are equivalent: res cor (i) hq−1 (K) −→ hq−1 (L)G −→ hq−1 (K) is exact. ∪b res (ii) hq−1 (K) −→ hq (K) −→ hq (L) is exact. Geometry & Topology Monographs, Volume 3 (2000) – Invitation to higher local fields Part I. Section 4. Cohomological symbol for henselian discrete valuation field 49 Proof. This is a property of the cup product of Galois cohomologies for L/K .