LECTURE NOTES / References
Iwasawa Theory
Romyar Sharifi
Bibliography
- [AB]
- M. Auslander and D. A. Buchsbaum, Unique factorization in regular local rings, Proc. Natl. Acad. Sci. USA 45 (1959), 733–734. (DOI)
- [Ba]
- A. Baker, Linear forms in the logarithms of algebraic numbers, Mathematika 13 (1966), 204–216. (DOI)
- [Br]
- A. Brumer, On the units of algebraic number fields, Mathematika 14 (1967), 121–124. (DOI)
- [CL]
- J. Coates and S. Lichtenbaum, On -adic zeta functions, Ann. of Math. (2) 98 (1973), 498–550. (DOI)
- [CW]
- J. Coates and A. Wiles, On -adic -functions and elliptic units, J. Austral. Math. Soc. Ser. A 26 (1978), 1–25. (DOI)
- [Co]
- R. F. Coleman, Division values in local fields, Invent. Math. 53 (1979), 91–116. (DOI)
- [FG]
- B. Ferrero and R. Greenberg, On the behavior of -adic -functions at , Invent. Math. 50 (1978), 91–102. (DOI)
- [FW]
- B. Ferrero and L. C. Washington, The Iwasawa invariant vanishes for abelian number fields, Ann. of Math. (2) 109 (1979), 377–395. (DOI)
- [Gr1]
- R. Greenberg, On -adic -functions and cyclotomic fields, Nagoya Math. J. 56 (1974), 61–77. (DOI)
- [Gr2]
- R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263–284. (DOI)
- [Ha]
- H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952.
- [He]
- J. Herbrand, Sur les classes des corps circulaires, J. Math. Pures Appl. (9) 11 (1932), 417–441.
- [Hi]
- H. Hida, Galois representations into attached to ordinary cusp forms, Invent. Math. 85 (1986), 545–613. (DOI)
- [Iw0]
- K. Iwasawa, On some invariants of cyclotomic fields, Amer. J. Math. 80 (1958), 773–783. (DOI) Erratum, 81 (1959), 280. (DOI)
- [Iw1]
- K. Iwasawa, On -extensions of algebraic number fields, Bull. Amer. Math. Soc. 65 (1959), 183–226. (DOI)
- [Iw2]
- K. Iwasawa, A class number formula for cyclotomic fields, Ann. of Math. (2) 76 (1962), 171–179. (DOI)
- [Iw3]
- K. Iwasawa, On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan 16 (1964), 42–82. (DOI)
- [Iw4]
- K. Iwasawa, On -adic -functions, Ann. of Math. (2) 89 (1969), 198–205. (DOI)
- [Iw5]
- K. Iwasawa, On some infinite abelian extensions of algebraic number fields, in Actes du Congrès International des Mathématiciens (Nice, 1970), tome 1, Gauthier-Villars, Paris, 1971, 391–394.
- [Iw6]
- K. Iwasawa, On -extensions of algebraic number fields, Ann. of Math. (2) 98 (1973), 246–326. (DOI)
- [Ka]
- K. Kato, -adic Hodge theory and values of zeta functions of modular forms, Astérisque 295 (2004), 117–290.
- [Ki]
- Y. Kida, -extensions of CM-fields and cyclotomic invariants, J. Number Theory 12 (1980), 519–528. (DOI)
- [KL]
- T. Kubota and H.-W. Leopoldt, Eine -adische Theorie der Zetawerte. Teil I: Einführung der -adischen Dirichletschen -Funktionen, J. Reine Angew. Math. 214/215 (1964), 328–339. (DOI)
- [Ko]
- V. A. Kolyvagin, Euler systems, in The Grothendieck Festschrift, vol. II, Progress in Mathematics 87, Birkhäuser, Boston, 1990, 435–483.
- [Le1]
- H.-W. Leopoldt, Zur Struktur der -Klassengruppe galoisscher Zahlkörper, J. Reine Angew. Math. 199 (1958), 165–174. (DOI)
- [Le2]
- H.-W. Leopoldt, Zur Arithmetik in abelschen Zahlkörpern, J. Reine Angew. Math. 209 (1962), 54–71. (DOI)
- [Ma]
- K. Mahler, An interpolation series for continuous functions of a -adic variable, J. Reine Angew. Math. 199 (1958), 23–34. (DOI)
- [MW]
- B. Mazur and A. Wiles, Class fields of abelian extensions of , Invent. Math. 76 (1984), 179–330. (DOI)
- [Oh]
- M. Ohta, Ordinary -adic étale cohomology groups attached to towers of elliptic modular curves. II, Math. Ann. 318 (2000), 557–583. (DOI)
- [Ri]
- K. A. Ribet, A modular construction of unramified -extensions of , Invent. Math. 34 (1976), 151–162. (DOI)
- [Ru]
- K. Rubin, The main conjectures of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25–68. (DOI)
- [Sh]
- R. T. Sharifi, Iwasawa modules in procyclic extensions, appendix to Y. Hachimori and R. Sharifi, On the failure of pseudo-nullity of Iwasawa modules, J. Algebraic Geom. 14 (2005), 567–591. (DOI)
- [Si]
- W. Sinnott, On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. (2) 108 (1978), 107–134. (DOI)
- [SU]
- C. Skinner and E. Urban, The Iwasawa main conjectures for , Invent. Math. 195 (2014), 1–277. (DOI)
- [St]
- L. Stickelberger, Ueber eine Verallgemeinerung der Kreistheilung, Math. Ann. 37 (1890), 321–367. (DOI)
- [Ta]
- J. Tate, Duality theorems in Galois cohomology over number fields, in Proceedings of the International Congress of Mathematicians, Stockholm, 1962, Institut Mittag-Leffler, Djursholm, 1963, 288–295.
- [Th]
- F. Thaine, On the ideal class groups of real abelian number fields, Ann. of Math. (2) 128 (1988), 1–18. (DOI)
- [We]
- H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313–352. (DOI)
- [Wi]
- A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131 (1990), 493–540. (DOI)