Geodesic
Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory
Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 527-543

Voir la notice de l'article provenant de la source Cambridge University Press

Let F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing H l(F, p) x H l (F, p) → H 2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.
DOI : 10.4153/CJM-1995-029-4
Mots-clés : 12, 16 
Hwangk, Yoon Sung; Jacob, Bill. Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory. Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 527-543. doi: 10.4153/CJM-1995-029-4
@article{10_4153_CJM_1995_029_4,
     author = {Hwangk, Yoon Sung and Jacob, Bill},
     title = {Brauer {Group} {Analogues} of {Results} {Relating} the {Witt} {Ring} to {Valuations} and {Galois} {Theory}},
     journal = {Canadian journal of mathematics},
     pages = {527--543},
     year = {1995},
     volume = {47},
     number = {3},
     doi = {10.4153/CJM-1995-029-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-029-4/}
}
TY  - JOUR
AU  - Hwangk, Yoon Sung
AU  - Jacob, Bill
TI  - Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory
JO  - Canadian journal of mathematics
PY  - 1995
SP  - 527
EP  - 543
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-029-4/
DO  - 10.4153/CJM-1995-029-4
ID  - 10_4153_CJM_1995_029_4
ER  - 
%0 Journal Article
%A Hwangk, Yoon Sung
%A Jacob, Bill
%T Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory
%J Canadian journal of mathematics
%D 1995
%P 527-543
%V 47
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1995-029-4/
%R 10.4153/CJM-1995-029-4
%F 10_4153_CJM_1995_029_4

[AEJ] Arason, J., Elman, R. and Jacob, B., Rigid Elements, valuations, and realization of Witt rings, J. Algebra 110(1987), 449–467. Google Scholar

[B] Becker, E., Formal-reelle Kôrper mit streng-auflösbarer absoluter Galoisgruppe, Math. Ann. 238(1978), 203–206. Google Scholar

[J] Jacob, B., Quadratic forms over Dyadic Valued Fields II, Relative Rigidity and Galois Cohomology, J. Algebra 148(1992), 162–202. Google Scholar

[JWd] Jacob, B. and Wadsworth, A., A New Construction of Nuncrossed Product Algebras, Trans. Amer. Math. Soc. 293(1986), 693–721. Google Scholar

[JWr 1] Jacob, B. and Ware, R., A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings, Math. Z. 200(1989), 379–396. Google Scholar

[JWr 2] Jacob, B., Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groups, Math. Z. 208(1991), 193–208. Google Scholar

[L] Lam, T.-Y., Algebraic Theory of Quadratic Forms, W. A. Benjamin Inc., 1973. Google Scholar

[K] Kato, K., A generalization of local class field theory by using K-groups, I, II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. (2) 26(1979), 303–376. (3) 27(1980), 603–683. Google Scholar

[M 1] Marshall, M., Abstract Witt Rings, Queen's Papers in Pure and Appl. Math. 57, 1980. Google Scholar

[M 2] Marshall, M., Classification of finitely generated Witt rings which are strongly representational, preprint. Google Scholar

[MY] Marshall, M. and Yucas, J., Linked quaternionic mappings and their associated Witt rings, Pacific J. Math. 95(1981), 411–426. Google Scholar

[Me] Merkmjev, A.S., K2 and the Brauer Group, Contemp. Math. 55(1986), 529–547. Google Scholar

[W 1] Ware, R., Quadratic Forms and Profinite 2-groups, J. Algebra 58(1979), 227–237. Google Scholar

[W 2] Ware, R., Valuation Rings and rigid elements infields, Canad. J. Math. 33(1981), 1338–1355. Google Scholar

Cité par Sources :