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Book Review

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Book Information:

Author: Victor P. Snaith
Title: Galois module structure
Additional book information: Fields Institute Monographs, vol. 2, American Mathematical Society, Providence, RI, 1994, vii+207 pp., $70.00, ISBN 0-8218-0264-X

[BB] Ph. Cassou-Noguès, T. Chinburg, A. Fröhlich, and M. J. Taylor, 𝐿-functions and Galois modules, 𝐿-functions and arithmetic (Durham, 1989) London Math. Soc. Lecture Note Ser., vol. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 75–139. Based on notes by D. Burns and N. P. Byott. MR 1110391, https://doi.org/10.1017/CBO9780511526053.005
[BF1] D. Burns, M. Flach, Motivic L-functions and Galois module structures, Math. Ann. 305 (1996), 65-102. CMP 96:11
[BF2] D. Burns, M. Flach, On Galois structure invariants associated to Tate motives (to appear).
[C1] T. Chinburg, On the Galois structure of algebraic integers and 𝑆-units, Invent. Math. 74 (1983), no. 3, 321–349. MR 724009, https://doi.org/10.1007/BF01394240
[C2] Ted Chinburg, Exact sequences and Galois module structure, Ann. of Math. (2) 121 (1985), no. 2, 351–376. MR 786352, https://doi.org/10.2307/1971177
[CKPS1] Ted Chinburg, Manfred Kolster, Georgios Pappas, and Victor Snaith, Galois structure of 𝐾-groups of rings of integers, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 12, 1435–1440 (English, with English and French summaries). MR 1340048
[CKPS2] T. Chinburg, M. Kolster, G. Pappas, V. Snaith, Galois structure of K-groups of rings on integers (to appear).
[F1] Albrecht Fröhlich, Galois module structure of algebraic integers, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 1, Springer-Verlag, Berlin, 1983. MR 717033
[F2] A. Fröhlich, Classgroups and Hermitian modules, Progress in Mathematics, vol. 48, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 756236
[H] David Holland, Additive Galois module structure and Chinburg’s invariant, J. Reine Angew. Math. 425 (1992), 193–218. MR 1151319, https://doi.org/10.1515/crll.1992.425.193
[K] Bruno Kahn, Descente galoisienne et 𝐾₂ des corps de nombres, 𝐾-Theory 7 (1993), no. 1, 55–100 (French, with English and French summaries). MR 1220427, https://doi.org/10.1007/BF00962794
[Ki1] Seyong Kim, A generalization of Fröhlich’s theorem to wildly ramified quaternion extensions of 𝑄, Illinois J. Math. 35 (1991), no. 1, 158–189. MR 1076672
[Ki2] Seyong Kim, The root number class and Chinburg’s second invariant, J. Algebra 153 (1992), no. 1, 133–202. MR 1195410, https://doi.org/10.1016/0021-8693(92)90152-C
[N] E. Nöether, Normalbasis bei Körpen ohne höhere Verzweigung, J. reine agnew. Math. 167 (1932), 147-152.
[Sn] Victor P. Snaith, Explicit Brauer induction, Cambridge Studies in Advanced Mathematics, vol. 40, Cambridge University Press, Cambridge, 1994. With applications to algebra and number theory. MR 1310780
[T] M. J. Taylor, On Fröhlich’s conjecture for rings of integers of tame extensions, Invent. Math. 63 (1981), no. 1, 41–79. MR 608528, https://doi.org/10.1007/BF01389193

Review Information:

Reviewer: A. Agboola
Affiliation: University of California, Santa Barbara
Email: agboola@math.ucsb.edu

Journal: Bull. Amer. Math. Soc. 35 (1998), 249-252
MSC (1991): Primary 11R04, 11R33, 11R37; Secondary 11R70, 19F99
DOI: https://doi.org/10.1090/S0273-0979-98-00753-8
Review copyright: © Copyright 1998 American Mathematical Society