Front Matter......Page 1
K. Iwasawa Princeton, 1986......Page 4
First page of Iwasawa's mauscript on cyclotomic fields [62]......Page 6
Contents......Page 8
Preface......Page 12
Introduction......Page 14
Acknowledgements......Page 15
John Coates, lwasawa's work in algebraic number theory......Page 16
[1] Ueber die Struktur der endlichen Gruppen,deren echte Untergruppen sämtlich nilpotent sind, Proc. Phys.-Math. Soc. Japan, 23-1 (1941), 1-4.......Page 27
[2] Über die Einfachheit der speziellen projektiven Gruppen, Proc. Imp. Acad. Japan, 17-3 (1941), 57-59.......Page 31
[3] Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Fac. Sci. Tokyo lmp. Univ., Sect I. 4-3 (1941), 171-199.......Page 34
[4] On almost periodic functions, Isô Sûgaku, 4-2 (10/1942), 56-60.......Page 63
[5] On normed rings and a theorem of Segal, I, Zenkoku Shijo Sugaku Danwakai, 246 (12/1942), 1522-1555......Page 70
[6] On the structure of infinite M-groups, Japanese J. Math., 18 (1943), 709-728.......Page 87
[7] On the structure of conditionally complete lattice-groups, Japanese J. Math., 18 (1943), 777-789.......Page 107
[8] Einige Sätze über freie Gruppen, Proc. Imp. Acad. Japan, 19-6 (1943), 272-274.......Page 120
[9] On one-parameter families of probability laws, J. Phys.-Math. Soc. Japan, 17-6 (1943}, 217-220......Page 123
[10] On normed rings and a theorem of Segal, II, Zenkoku Shijo Sugaku Danwakai, 251 (3/1943), 167-186......Page 128
[11] On group rings of topological groups, Proc. Imp. Acad. Japan, 20-2 (1944), 67-70.......Page 140
[12] Über nilpotente topologische Gruppen I, Proc. Japan Acad., 21-3 (1945), 124-137.......Page 144
[13] Der Bezoutsche Satz in zweifach projektiven Räumen, Proc. Japan Acad., 21-4 (1945), 213-222.......Page 158
[14] Zur Theorie der algebraischen Korrespondenzen I, Schnittpunktgruppen von Korrespondenzen, Proc. Japan Acad., 21-4 (1945), 204-212.......Page 168
[15] Zur Theorie der algebraischen Korrespondenzen II, Multiplikation der Korrespondenzen, Proc. Japan Acad., 21-9 (1945), 411-418.......Page 177
[16] On the representation of Lie algebras, Japanese J. Math., 19 (1948), 405-426.......Page 185
[17] On linearly ordered groups, J. Math. Soc. Japan, 1-9 (1948), 1-9.......Page 207
[18] Finite groups and compact groups, Sûgaku, 1-2 (3/1948), 94-95......Page 216
[19] Hilbert's fifth problem, Sûgaku, 1-3 (11/1948), 161-171......Page 219
[20] (with T. Tamagawa) Automorphisms of a function field, Sûgaku, 1-4 (1/1949), 315-316.......Page 231
[21] On some types of topological groups, Ann. of Math., (2) 50 (1949), 507-558.......Page 233
[22] Topological groups with invariant compact neighborhoods of the identity, Ann. of Math., (2) 54 (1951), 345-348.......Page 285
[23] A note on L-functions, "Proc. Int. Congress of Math." (Cambridge, Mass., 1950), Vol.1, Amer. Math. Soc., 1952, p. 322.......Page 289
[24] Some properties of (L)-groups, Proc. Int. Congress of Math. (Cambridge, Mass., 1950), Vol.2, Amer. Math. Soc., 1952, pp. 447-450.......Page 290
[25] (with T. Tamagawa) On the group of automorphisms of a function field, J. Math. Soc. Japan, 3 (1951), 137-147. Corrections, ibid., 4 (1952),100-101, 203-204.......Page 294
[26] On the rings of valuation vectors, Ann. of Math., (2) 57 (1953), 331-356.......Page 309
[27] On solvable extensions of algebraic number fields, Ann. of Math., (2) 58 (1953), 548-572.......Page 335
[28] A note on Kummer extensions, J. Math. Soc. Japan, 5 (1953), 253-262.......Page 360
[29] On Galois groups of local fields, Trans. Amer. Math. Soc., 80 (1955), 448-469.......Page 370
[30] Galois groups acting on the multiplicative groups of local fields, "Proc. Int. Sympos. on Algebraic Number Theory" (Tokyo and Nikko, 1955), Science Council of Japan, Tokyo, 1956, pp. 63-64.......Page 392
[31] A note on the group of units of an algebraic number field, J. Math. Pure and Appl., (9) 35 (1956), 189-192.......Page 394
[32] A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258.......Page 398
[33] On some invariants of cyclotomic fields, Amer. J. Math., 80 (1958), 773-783. Erratum, ibid., 81 (1959), 280.......Page 400
[34] Sheaves for algebraic number fields, Ann. of Math., (2) 69 (1959), 408-413.......Page 412
[35] On \Gamma-extensions of algebraic number fields, Bull. Amer. Math. Soc., 65 (1959), 183-226.......Page 418
[36] On some properties of \Gamma-finite modules, Ann. of Math., (2) 70 (1959), 291-312.......Page 462
[37] On the theory of cyclotomic fields, Ann. of Math., (2) 70 (1959), 530-561.......Page 484
[38] On local cyclotomic fields, J. Math. Soc. Japan, 12 (1960), 16-21.......Page 516
[39] A class number formula for cyclotomic fields, Ann. of Math., (2) 76 (1962), 171-179.......Page 522
[40] On a certain analogy between algebraic number fields and function fields, Sûgaku, 15-2 (10/1963), 65-67......Page 531
[41] On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42-82.......Page 535
[42] Some results in the theory of cyclotomic fields, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., 1965, pp. 66-69.......Page 576
[43] (with C. C. Sims) Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan, 18 (1966), 86-96.......Page 580
[44] A note on ideal class groups, Nagoya Math J., 27 (1966), 239-247.......Page 591
[45] Some modules in local cyclotomic fields, "Les Tendances Géom. en Algèbre et Théorie des Nombres", Éditions du Centre National de la Recherche Scientifique, Paris,1966, pp. 87-96.......Page 600
[46] On explicit formulas for the norm residue symbol, J. Math. Soc. Japan, 20 (1968), 151-165.......Page 610
[47] Analogies between number fields and function fields, "Some Recent Advances in the Basic Sciences, Proc. Annual Sci. Conf." (New York, 1965-1966), Vol. 2, Belfer Grad. School Sci.,Yeshiva Univ., New York, 1969, pp. 203-208.......Page 625
[48] On p-adic L-functions, Ann. of Math., (2) 89 (1969), 198-205.......Page 631
[49] On some infinite Abelian extensions of algebraic number fields, "Actes du Congrés Int. Math." (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, pp. 391-394.......Page 639
[50] Skew-symmetric forms for number fields, Proc. Sympos. Pure Math., Vol. XX, Amer. Math. Soc., 1971, p. 86.......Page 643
[51] On the \mu-invariants of cyclotomic fields, Acta Arith., 21 (1972), 99-101.......Page 644
[52] On Z_$\ell$-extensions of algebraic number fields, Ann. of Math., (2) 98 (1973), 246-326.......Page 647
[53] On the \mu-invariants of Z_$ell$-extensions, "Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Yasuo Akizuki", Kinokuniya, Tokyo, 1973, pp. 1-11.......Page 728
[54] A note on Jacobi sums, "Convegno di Strutture in Corpi Algebrici" (Rome, 1973), INDAM, Symposia Mathematica, Vol, XV, Academic Press, London, 1975, pp. 447-459.......Page 739
[55] A note on cyclotomic fields, Invent. math., 36 (1976), 115-123.......Page 752
[56] Some remarks on Hecke characters, "Algebraic Number Theory" (Kyoto, 1976), Japan Soc. Promotion Sci., Tokyo, 1977, pp. 99-108.......Page 761
[57] On p-adic representations associated with Zp-extensions, "Automorphic Forms, Representation Theory and Arithmetic" (Bombay, 1979), Tata Inst. Fund. Res., Bombay, 1981, pp. 141-153.......Page 771
[58] Riemann-Hurwitz formula and p-adic Galois representations for number fields, Tôhoku Math. J., (2) 33 (1981), 263-288.......Page 784
[59] On cohomology groups of Zp-extensions, "Zp-extensions and Related Topics" (Kyoto, 6/1981; G. Fujisaki, ed.), Kokyuroku, No. 440, RIMS, Kyoto Univ., 1981, pp. 76-84......Page 810
[60] On cohomology groups of units for Zp-extensions, Amer. J. Math., 105 (1983), 189-200; "Geometry and Number Theory, A Volume in Honor of André Weil" (J.-P. Serre and G. Shimura eds.), The Johns Hopkins University Press, 1983, pp. 189-200.......Page 815
[61] A simple remark on Leopoldt's conjecture, "Report of the Conference on Algebraic Number theory" (RIMS, Kyoto, 7/1984; K. Shiratani, ed.), 1984, pp. 45-54......Page 827
[63] A note on capitulation problem for number fields, Proc. Japan Acad., 65-2, Ser. A (1989), 59-61.......Page 838
[64] A note on capitulation problem for number fields. II, Proc. Japan Acad., 65-6, Ser. A (1989), 183-186.......Page 841
[65] On papers of Takagi in number theory, "Teiji Takagi Collected Papers", Springer-Verlag Tokyo, 1990, Appendices, I, pp. 342-351.......Page 845
[66] A letter to J. Dieudonné, "Zeta Functions in Geometry"(Tokyo, 1990), Adv. St. in Pure Math., 21, 1992, pp. 445-450.......Page 855
[U1] A note on unitary representations, (lectured in a Colloquium at Kyoto Univ., Dec. 1987).......Page 861
[U2] Automorphisms of Galois groups over number fields, (lectured in the "Symposium on L-functions and Galois properties of algebraic number fields",
the Univ. of Durham, Sept. 1975).......Page 865
[U3] Some problems on cyclotomic fields and Zp-extensions, (lectured in "Arithmetik der ABELschen Zahlkörper und Klassenkörper der komplexen Multiplikation",
Math. Forschungsinstitut Oberwolfach, March 1979).......Page 871
[U4] A simple remark on Leopoldt's conjecture, (lectured in the "Conference on
Algebraic Number Theory", Res. Inst. Math. Sci., Kyoto Univ., July 1984).......Page 880
[U5] On integral representations of some finite groups, (lectured in Komaba seminar at the Univ. of Tokyo, June 1989).......Page 889
Bibliography......Page 893
Back Cover......Page 899
[A1] On groups and the associated lattices (909. 群トソノ lattice ニツイテ), ZSSD, 211(19410315), 76-81......Page 900
[A2] On groups and the associated lattices II (群とその lattice についてII), Iso
Sugaku (位相数学), 4-1 (2/1942), 47-50......Page 906
[A3] On groups and the associated lattices III (975. 群トソノ lattice ニツイテ III), ZSSD, 225(19411027), 519-542......Page 910
[A4] A remark on lattice groups (1029. 束群ニ関スル一注意), ZSSD, 234(19420323), 912-914......Page 934
[A5] On lattice groups (1044. 束群ニツイテ), ZSSD, 235(19420416), 1030-1048......Page 937
[A6] On a generalization of central series (1089. 核心群列ノ一拡張ニツイテ), ZSSD, 246(19421214), 1555-1563......Page 956
[A7] On the correspondence between groups and ideals in the group rings (1090. 群ト群環ニ於ケル Ideal トノ対応ニ就イテ), ZSSD, 246(19421214), 1563-1591......Page 965
[A8] A remark on solvable groups (1149. 可解群ニ関スル一注意), ZSSD, 258(19431025), 539-544......Page 994
[A9] An example of a group (1168. 群ノ一例), ZSSD, 262(19440320), 67-69......Page 1000
[A10] On faithful representations of a Lie algebra (23. Lie 環ノ同型表現ニツイテ), ZSSD (Ser.2), 3(19470220), 1-6......Page 1003
[A11] Review of "Theory of differential forms - Grassmann algebras and Lie groups (微分式論―グラスマン代数とリー群)" by Yukiyoshi Kawada (Kawade Shobo(河出書房), Tokyo,1951), Math. Reviews 14 (1953), 410......Page 1009
[A12] Review of "Allgemeine Theorie der algebraischen Zahlen" by Philipp Furtwängler (B. G. Teubner Verlagsgesellschaft, Leipzig, 1953), Math. Reviews 15 (1954), 404......Page 1010
[A13] Review of "Introduction to algebraic number theory" by Henry B. Mann (The Ohio State Univ. Press, Columbus, Ohio, 1955), Math. Reviews 17 (1956), 240-241......Page 1011
[A14] Review of "Topological transformation groups" by Deane Montgomery and Leo Zippin (Interscience Publishers, New York -London, 1955), Math. Reviews 17 (1956), 383-384......Page 1013
[A15] Review of Die Berechnung der Klasssenzahl Abelscher Körper über quadratischen Zahlkörpern by Curt Meyer (Akademie-Verlag, Berlin, 1957), Bull. Amer. Math. Soc., 64 (1958), 211-212......Page 1015
[A16] Impressions of the International Congress of Mathematicians, I (Congress印象記I), Sugaku (数学) 14-3 (2/1963), 174-175......Page 1017
[A17] Review of "Introduction to quadratic forms" by O. T. O'Meara (Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963), Math. Reviews 27 (1964), 482-483......Page 1019
[A18] On the mathematical works of Prof. Hiraku Toyama - around the thesis "Non-abelian theory of algebraic functions" (遠山啓教授の数学的業績ー学位論文「代数関数の非アーベル的理論」を中心に), Sugaku Seminar (数学セミナー) (3/1980), 24-28......Page 1021
[A19] 120 minutes with Prof. Kenkichi Iwasawa (Interview by the editors of Sugaku)(岩澤健吉先生のお話を伺った120分(編集部)), Sugaku(数学), 45-4 (101990), 366-372......Page 1026
Round-table talk with 3 overseas Japanese mathematicians (座談会・在外数学者の生活と意見), Sugaku Seminar (数学セミナー) (2/1963), 4-12......Page 1033
