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Taylor, M. J.

On Fröhlich’s conjecture for rings of integers of tame extensions. (English) Zbl 0469.12003

Invent. Math. 63, 41-79 (1981).
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Cited in 12 Reviews
Cited in 66 Documents

MSC:

11R32 Galois theory
11R18 Cyclotomic extensions

Keywords:

tame extensions; algebraic integers; class group; Artin root numbers

Citations:

Zbl 0359.12015; Zbl 0219.12012; Zbl 0261.12008; Zbl 0469.12002; Zbl 0368.12004; Zbl 0385.12003
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Full Text: DOI EuDML

References:

[1] [C] Cassou-Noguès, Ph.: Quelques théorèmes de base normale d’entiers, Ann. Inst. Fourier,28, 1-33 (1978) · Zbl 0368.12004
[2] [DH] Davenport, H., Hasse, H.: Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. J. reine und angew. Math.172, 151-182 (1935) · JFM 60.0913.01 · doi:10.1515/crll.1935.172.151
[3] [D] Deligne, P.: Les constantes des équations fonctionnelles des fonctionsL, Modular Forms in one variable, Lecture Notes in Mathematics349, 501-597 (1973) · doi:10.1007/978-3-540-37855-6_7
[4] [F1] Fröhlich, A.: Arithmetic and Galois module structure for tame extensions, J. reine angew. Math.286, 380-440 (1976) · Zbl 0385.12004 · doi:10.1515/crll.1976.286-287.380
[5] [F3] Fröhlich, A.: Locally free modules over arithmetic orders, J. reine angew. Math.274, 112-124 (1975) · Zbl 0316.12013 · doi:10.1515/crll.1975.274-275.112
[6] [F4] Fröhlich, A.: Classgroups, in particular Hermitian classgroups, in press (1980)
[7] [F5] Fröhlich, A.: Artin root numbers and normal integral bases for quaternion fields, Invent. Math.17, 143-166 (1972) · Zbl 0261.12008 · doi:10.1007/BF01418937
[8] [F6] Fröhlich, A.: Module Invariants and root numbers for quaternion fields of degree 4l’, Proc. Camb. Phil. Soc.76, 393-399 (1974) · Zbl 0304.12008 · doi:10.1017/S0305004100049069
[9] [FT] Fröhlich, A., Taylor, M.J.: The arithmetic theory of local Galois Gauss sums for tame characters, Philosophical Transactions of the Royal Society298, 141-181 (1980) · Zbl 0436.12014 · doi:10.1098/rsta.1980.0242
[10] [M1] Martinet, J.: Modules sur l’algèbre du groupe quaternonien, Ann. Sci. Ecole Norm. Sup.4, 229-308 (1971)
[11] [M2] Martinet, J.: Character theory and ArtinL-functions, Algebraic Number Fields (Proc. Durham Symposium). London: Academic Press 1977
[12] [N] Noether, E.: Normalbasis bei Körpern ohne höhere Verzweigung, J. reine angew. Math.167, 147-152 (1932) · JFM 58.0172.02 · doi:10.1515/crll.1932.167.147
[13] [S] Serre, J-P.: Représentations linéaires des groupes finis. 2nd edition. Paris: Hermann 1971
[14] [T1] Taylor, M.J.: A logarithmic approach to classgroups of integral group rings, J. Algebra,66, 321-353 (1980) · Zbl 0491.12007 · doi:10.1016/0021-8693(80)90092-7
[15] [T2] Taylor, M.J.: Galois module structure of relative abelian extensions, J. reine angew. Math.303, 97-101 (1978) · Zbl 0384.12007 · doi:10.1515/crll.1978.303-304.97
[16] [T3] Taylor, M.J.: Adams operations, local root numbers and the Galois module structure of rings of integers, Proc. L.M.S. (3),39, 147-175 (1979) · Zbl 0424.12007 · doi:10.1112/plms/s3-39.1.147
[17] [U] Ullom, S.: Character action on the classgroup of Fröhlich, informal report
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