Collected Papers (Springer Collected Works in Mathematics) (English, Japanese and German Edition)

Kenkichi Iwasawa was one of the most original and influential mathematicians of the twentieth century. He made a number of fundamental contributions in group theory and algebraic number theory. In group theory, he created the theory of ( L )-groups (including the structure theorem called "Iwasawa decomposition"), which played an important role in the solution of Hilbert's Fifth Problem. In number theory, he constructed a beautiful theory on Z p -extensions, now called "Iwasawa theory", realizing the deep analogy between number fields and algebraic function fields. Iwasawa theory has had a strong influence on the recent development of arithmetic algebraic geometry, including the solution of Fermat's Last Theorem. This volume of the collected papers of K. Iwasawa contains all 66 of his published papers, including 11 papers in Japanese, for which English abstracts by the editors are attached. In addition, the volume contains 5 papers unpublished until 2001. Also included is a masterly summary of Iwasawa theory by J. Coates (The University of Cambridge). Front Matter K. Iwasawa Princeton, 1986 First page of Iwasawa's mauscript on cyclotomic fields [62] Contents Preface Introduction Acknowledgements John Coates, lwasawa's work in algebraic number theory Papers [1] Ueber die Struktur der endlichen Gruppen,deren echte Untergruppen sämtlich nilpotent sind, Proc. Phys.-Math. Soc. Japan, 23-1 (1941), 1-4. [2] Über die Einfachheit der speziellen projektiven Gruppen, Proc. Imp. Acad. Japan, 17-3 (1941), 57-59. [3] Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Fac. Sci. Tokyo lmp. Univ., Sect I. 4-3 (1941), 171-199. [4] On almost periodic functions, Isô Sûgaku, 4-2 (10/1942), 56-60. [5] On normed rings and a theorem of Segal, I, Zenkoku Shijo Sugaku Danwakai, 246 (12/1942), 1522-1555 [6] On the structure of infinite M-groups, Japanese J. Math., 18 (1943), 709-728. [7] On the structure of conditionally complete lattice-groups, Japanese J. Math., 18 (1943), 777-789. [8] Einige Sätze über freie Gruppen, Proc. Imp. Acad. Japan, 19-6 (1943), 272-274. [9] On one-parameter families of probability laws, J. Phys.-Math. Soc. Japan, 17-6 (1943}, 217-220 [10] On normed rings and a theorem of Segal, II, Zenkoku Shijo Sugaku Danwakai, 251 (3/1943), 167-186 [11] On group rings of topological groups, Proc. Imp. Acad. Japan, 20-2 (1944), 67-70. [12] Über nilpotente topologische Gruppen I, Proc. Japan Acad., 21-3 (1945), 124-137. [13] Der Bezoutsche Satz in zweifach projektiven Räumen, Proc. Japan Acad., 21-4 (1945), 213-222. [14] Zur Theorie der algebraischen Korrespondenzen I, Schnittpunktgruppen von Korrespondenzen, Proc. Japan Acad., 21-4 (1945), 204-212. [15] Zur Theorie der algebraischen Korrespondenzen II, Multiplikation der Korrespondenzen, Proc. Japan Acad., 21-9 (1945), 411-418. [16] On the representation of Lie algebras, Japanese J. Math., 19 (1948), 405-426. [17] On linearly ordered groups, J. Math. Soc. Japan, 1-9 (1948), 1-9. [18] Finite groups and compact groups, Sûgaku, 1-2 (3/1948), 94-95 [19] Hilbert's fifth problem, Sûgaku, 1-3 (11/1948), 161-171 [20] (with T. Tamagawa) Automorphisms of a function field, Sûgaku, 1-4 (1/1949), 315-316. [21] On some types of topological groups, Ann. of Math., (2) 50 (1949), 507-558. [22] Topological groups with invariant compact neighborhoods of the identity, Ann. of Math., (2) 54 (1951), 345-348. [23] A note on L-functions, Proc. Int. Congress of Math. (Cambridge, Mass., 1950), Vol.1, Amer. Math. Soc., 1952, p. 322. [24] Some properties of (L)-groups, Proc. Int. Congress of Math. (Cambridge, Mass., 1950), Vol.2, Amer. Math. Soc., 1952, pp. 447-450. [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. [26] On the rings of valuation vectors, Ann. of Math., (2) 57 (1953), 331-356. [27] On solvable extensions of algebraic number fields, Ann. of Math., (2) 58 (1953), 548-572. [28] A note on Kummer extensions, J. Math. Soc. Japan, 5 (1953), 253-262. [29] On Galois groups of local fields, Trans. Amer. Math. Soc., 80 (1955), 448-469. [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. [31] A note on the group of units of an algebraic number field, J. Math. Pure and Appl., (9) 35 (1956), 189-192. [32] A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), 257-258. [33] On some invariants of cyclotomic fields, Amer. J. Math., 80 (1958), 773-783. Erratum, ibid., 81 (1959), 280. [34] Sheaves for algebraic number fields, Ann. of Math., (2) 69 (1959), 408-413. [35] On Gamma-extensions of algebraic number fields, Bull. Amer. Math. Soc., 65 (1959), 183-226. [36] On some properties of Gamma-finite modules, Ann. of Math., (2) 70 (1959), 291-312. [37] On the theory of cyclotomic fields, Ann. of Math., (2) 70 (1959), 530-561. [38] On local cyclotomic fields, J. Math. Soc. Japan, 12 (1960), 16-21. [39] A class number formula for cyclotomic fields, Ann. of Math., (2) 76 (1962), 171-179. [40] On a certain analogy between algebraic number fields and function fields, Sûgaku, 15-2 (10/1963), 65-67 [41] On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42-82. [42] Some results in the theory of cyclotomic fields, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., 1965, pp. 66-69. [43] (with C. C. Sims) Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan, 18 (1966), 86-96. [44] A note on ideal class groups, Nagoya Math J., 27 (1966), 239-247. [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. [46] On explicit formulas for the norm residue symbol, J. Math. Soc. Japan, 20 (1968), 151-165. [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. [48] On p-adic L-functions, Ann. of Math., (2) 89 (1969), 198-205. [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. [50] Skew-symmetric forms for number fields, Proc. Sympos. Pure Math., Vol. XX, Amer. Math. Soc., 1971, p. 86. [51] On the mu-invariants of cyclotomic fields, Acta Arith., 21 (1972), 99-101. [52] On Z_$ell$-extensions of algebraic number fields, Ann. of Math., (2) 98 (1973), 246-326. [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. [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. [55] A note on cyclotomic fields, Invent. math., 36 (1976), 115-123. [56] Some remarks on Hecke characters, Algebraic Number Theory (Kyoto, 1976), Japan Soc. Promotion Sci., Tokyo, 1977, pp. 99-108. [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. [58] Riemann-Hurwitz formula and p-adic Galois representations for number fields, Tôhoku Math. J., (2) 33 (1981), 263-288. [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 [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. [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 [63] A note on capitulation problem for number fields, Proc. Japan Acad., 65-2, Ser. A (1989), 59-61. [64] A note on capitulation problem for number fields. II, Proc. Japan Acad., 65-6, Ser. A (1989), 183-186. [65] On papers of Takagi in number theory, Teiji Takagi Collected Papers, Springer-Verlag Tokyo, 1990, Appendices, I, pp. 342-351. [66] A letter to J. Dieudonné, ''Zeta Functions in Geometry''(Tokyo, 1990), Adv. St. in Pure Math., 21, 1992, pp. 445-450. Unpublished papers [U1] A note on unitary representations, (lectured in a Colloquium at Kyoto Univ., Dec. 1987). [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). [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). [U4] A simple remark on Leopoldt's conjecture, (lectured in the ''Conference on Algebraic Number Theory'', Res. Inst. Math. Sci., Kyoto Univ., July 1984). [U5] On integral representations of some finite groups, (lectured in Komaba seminar at the Univ. of Tokyo, June 1989). Bibliography Back Cover Articles not included in these volumes [A1] On groups and the associated lattices (909. .... lattice ....), ZSSD, 211(19410315), 76-81 [A2] On groups and the associated lattices II (.... lattice ....II), Iso Sugaku (....), 4-1 (2/1942), 47-50 [A3] On groups and the associated lattices III (975. .... lattice .... III), ZSSD, 225(19411027), 519-542 [A4] A remark on lattice groups (1029. .........), ZSSD, 234(19420323), 912-914 [A5] On lattice groups (1044. ......), ZSSD, 235(19420416), 1030-1048 [A6] On a generalization of central series (1089. ............), ZSSD, 246(19421214), 1555-1563 [A7] On the correspondence between groups and ideals in the group rings (1090. ........ Ideal ........), ZSSD, 246(19421214), 1563-1591 [A8] A remark on solvable groups (1149. ..........), ZSSD, 258(19431025), 539-544 [A9] An example of a group (1168. ....), ZSSD, 262(19440320), 67-69 [A10] On faithful representations of a Lie algebra (23. Lie ..........), ZSSD (Ser.2), 3(19470220), 1-6 [A11] Review of ''Theory of differential forms - Grassmann algebras and Lie groups (................)'' by Yukiyoshi Kawada (Kawade Shobo(....), Tokyo,1951), Math. Reviews 14 (1953), 410 [A12] Review of ''Allgemeine Theorie der algebraischen Zahlen'' by Philipp Furtwängler (B. G. Teubner Verlagsgesellschaft, Leipzig, 1953), Math. Reviews 15 (1954), 404 [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 [A14] Review of ''Topological transformation groups'' by Deane Montgomery and Leo Zippin (Interscience Publishers, New York -London, 1955), Math. Reviews 17 (1956), 383-384 [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 [A16] Impressions of the International Congress of Mathematicians, I (Congress...I), Sugaku (..) 14-3 (2/1963), 174-175 [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 [A18] On the mathematical works of Prof. Hiraku Toyama - around the thesis ''Non-abelian theory of algebraic functions'' (...................................), Sugaku Seminar (......) (3/1980), 24-28 [A19] 120 minutes with Prof. Kenkichi Iwasawa (Interview by the editors of Sugaku)(.............120.(...)), Sugaku(..), 45-4 (101990), 366-372 Round-table talk with 3 overseas Japanese mathematicians (...............), Sugaku Seminar (......) (2/1963), 4-12 Iwasawa Is One Of The Most Original And Influential Mathematicians In The 20th Century. This Collected Papers Of K. Iwasawa Contains All 66 Published Papers, Including 11 Papers In Japanese, For Which English Abstracts (by The Editors) Are Attached. Also Included Is A Masterly Summery Of Iwasawa Theory By J. Coates (cambridge).