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Book Review

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Book Information

Author(s): Ido Efrat
Title: Valuations, orderings and Milnor $ K$-theory
Additional book information: Mathematical Surveys and Monographs, vol. 124, American Mathematical Society, Providence, RI, 2006, xiv+288, US$60.00, 978-0-8218-4041-2

References:

[A-E-J]
J. Arason, R. Elman, B. Jacob, Rigid elements, valuations, and realization of Witt rings, J. Algebra 110 (1987), 449-467. MR 0910395 (89a:11041)

[B-B]
E. Becker, L. Bröcker, On the description of the reduced Witt ring, J. Algebra 52 (1978), 328-346. MR 0506029 (58:21935)

[B-R]
E. Becker, A. Rosenberg, Reduced forms and reduced Witt rings of higher level, J. Algebra 92 (1985), 477-503. MR 0778463 (86e:11029)

[B1]
L. Bröcker, Zur Theorie der quadratischen Formen über formal reellen Körpern, Math. Ann. 210 (1974), 233-256. MR 0354549 (50:7027)

[B2]
-, Characterization of fans and hereditarily Pythagorean fields, Math. Z. 151 (1976), 149-163. MR 0422233 (54:10224)

[C]
T. Craven, Characterizing reduced Witt rings of fields, J. Algebra 53 (1978), 74-96. MR 0480332 (58:505)

[E]
I. Efrat, Orderings, valuations and free products of Galois groups, Sém. Struct. Alg. Ordonnées 54, Univ. Paris 7 (1995).

[H-J]
Y.S. Hwang, B. Jacob, Brauer group analogues of results relating the Witt ring to valuations and Galois theory, Canad. J. Math. 47 (1995), 527-543. MR 1346152 (97a:12004)

[J-W1]
B. Jacob, R. Ware, A recursive description of the maximal pro-$ 2$ Galois group via Witt rings, Math. Z. 200 (1989), 379-396. MR 0978598 (90b:11127)

[J-W2]
-, Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groups, Math. Z. 208 (1991), 193-208. MR 1128705 (92h:11032)

[Ko]
J. Koenigsmann, From $ p$-rigid elements to valuations (with a Galois-characterization of $ p$-adic fields), J. Reine Angew. Math. 465 (1995), 165-182. MR 1344135 (96m:12003)

[Ku]
M. Kula, Fields with prescribed quadratic form schemes, Math. Z. 167 (1979), 201-212. MR 0539104 (80f:10024)

[L]
T.-Y. Lam, Orderings, valuations and quadratic forms, CBMS 52, Amer. Math. Soc., 1983. MR 0714331 (85e:11024)

[M1]
M. Marshall, The elementary type conjecture in quadratic form theory, Cont. Math. 344 (2004), 275-293. MR 2060204 (2005b:11046)

[M2]
-, Real reduced multirings and multifields, J. Pure and Applied Algebra 205 (2006), 452-468. MR 2203627 (2006k:14110)

[M-S]
A.S. Merkurjev, A.A. Suslin, $ K$-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 1011-1046 (Russian); Math. USSR Izv. 21 (1983), 307-340 (English translation). MR 0675529 (84i:12007)

[Mi]
J. Milnor, Algebraic K-theory and quadratic forms, Invent. Math. 9 (1970), 318-344. MR 0260844 (41:5465)

[Mi-S]
J. Minác, T. Smith, Decomposition of Witt rings and Galois groups, Canad. J. Math. 47 (1995), 1274-1289. MR 1370518 (96k:11048)

[Pf]
A. Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. (1966), 116-132. MR 0200270 (34:169)

[Po]
V. Powers, Characterizing reduced Witt rings of higher level, Pac. J. Math. 128 (1987), 333-347. MR 0888522 (88d:11038)

[Pr]
A. Prestel, Lectures on formally real fields, IMPA Lecture Notes 22, Rio de Janeiro, 1975, Lecture Notes in Math. 1093, Springer, 1984. MR 0769847 (86h:12013)

[V1]
V. Voevodsky, Motivic cohomology with $ \mathbb{Z}/2$-coefficients, Publ. Math. IHES 98 (2003), 59-104. MR 2031199 (2005b:14038b)

[V2]
-, On motivic cohomology with $ \mathbb{Z}/\ell $-coefficients, preprint.

[W]
E. Witt, Theorie der Quadratischen Formen in beliebigen Körpern, J. Reine Angew. Math. 176 (1937), 31-44.

Additional Information:

Reviewer(s):
Murray Marshall
Affiliation: University of Saskatchewan
Email: marshall@math.usask.ca

Review Information:
Journal: Bull. Amer. Math. Soc. 45 (2008), 439-444.

MSC (2000): Primary 12J10, 12J15, 19D45
PII: S 0273-0979(07)01166-4
Posted: August 3, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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