American Mathematical Society

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

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, DOI 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).

T. Chinburg, On the Galois structure of algebraic integers and $S$-units, Invent. Math. 74 (1983), no. 3, 321–349. MR 724009, DOI 10.1007/BF01394240

Ted Chinburg, Exact sequences and Galois module structure, Ann. of Math. (2) 121 (1985), no. 2, 351–376. MR 786352, DOI 10.2307/1971177

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).

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, DOI 10.1007/978-3-642-68816-4

A. Fröhlich, Classgroups and Hermitian modules, Progress in Mathematics, vol. 48, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 756236, DOI 10.1007/978-1-4684-6740-6

David Holland, Additive Galois module structure and Chinburg’s invariant, J. Reine Angew. Math. 425 (1992), 193–218. MR 1151319, DOI 10.1515/crll.1992.425.193

Bruno Kahn, Descente galoisienne et $K_2$ des corps de nombres, $K$-Theory 7 (1993), no. 1, 55–100 (French, with English and French summaries). MR 1220427, DOI 10.1007/BF00962794

Seyong Kim, A generalization of Fröhlich’s theorem to wildly ramified quaternion extensions of $\textbf {Q}$, Illinois J. Math. 35 (1991), no. 1, 158–189. MR 1076672

Seyong Kim, The root number class and Chinburg’s second invariant, J. Algebra 153 (1992), no. 1, 133–202. MR 1195410, DOI 10.1016/0021-8693(92)90152-C

[N]

E. Nöether, Normalbasis bei Körpen ohne höhere Verzweigung, J. reine agnew. Math. 167 (1932), 147-152.

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, DOI 10.1017/CBO9780511600746

M. J. Taylor, On Fröhlich’s conjecture for rings of integers of tame extensions, Invent. Math. 63 (1981), no. 1, 41–79. MR 608528, DOI 10.1007/BF01389193

Review Information:

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