Bibliography

Bibliography

Bibliography Comments Introductory sources on related subjects. local fields [Cas]; algebraic number theory [KKS], [M], [N5], [NSchW], [CF], [FT], [BSh], [Iya], [La2], [IR], [Ko6], [W]; cyclotomic fields [Wa], [La3]; valuation theory [E], [Rib]; history of [Roq3]; formally -adic fields [PR]; non-Archimedean analysis [Kob1–2], [vR], [Schf], [T4], [BGR]; embedding problems [ILF]; formal groups [Fr], [CF], [Iw6], [Haz3]; elliptic curves over number fields [Silv]; local zeta function and Fourier analysis [T1], [RV], [Ig], [Den]; -adic ¡ -functions [Wa], [Iw7], [Hi]; local Langlands correspondence [T7], [Bum], [Kudl], [BaK], [Rit2]; pro- -groups [DdSMS], [Wi], [dSSS]; -adic Hodge theory [T2], [Fo2], [Sen4,7–9]; -adic periods [A]; -adic differential equations [RC]; non-Archimedean analytic geometry [Ber]; field arithmetic [FJ], [Jar], [Ef4]; characteristic [Gos]; Milnor ¢ -theory [Bas], [Ro], [Silr], [Gr]; higher local fields and higher local class field theory [FK]; power series over local fields, formal groups, and dynamics [Lu1–2], [Li1–4]; non-Archimedean physics [VVZ], [BF], [Chr], [RTVW], [HS], [Kh]. Symbols and explicit formulas (perfect residue field case). [AH1–2], [Has1–11], [Sha2], [Kn], [Rot], [Bru1–2], [Henn1–2], [Iw3], [Col1,3], [Wil], [CW1], [dSh1–3], [Sen3], [Hel], [Des], [Shi], [Sue], [ShI], [V1–7,9], [Fe1–2], [BeV1–2], [Ab5–6], [Kol], [Kuz], [Kat6–7], [Ku3–4], [GK], [VG], [DV1–2], [Ben1–2]. 319 320 £¥¤§¦©¨ ¤ © Ramification theory of local fields (perfect residue field case). [Kaw1], [Sa], [Tam], [Hei], [Mar1], [Mau1–5], [Mik5–6], [T2], [Wy], [Sen1–2], [ST], [Ep], [KZ], [Fo4], [Win1–4], [Lau1–6], [LS], [CG], [Ab2–4,7–8], [Fe8,11–12]. Bibliography [A] Periodes´ -adiques, Asterisque´ , vol. 223, SMF, 1994. [Ab1] V. A. Abrashkin, Galois modules of group schemes of period over the ring of Witt vectors, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 4, 691–736; English transl. in Math. USSR-Izv. 31 (1988). [Ab2] , Ramification filtration of the Galois group of a local field, Tr. St-Peterbg. Mat. Obsch., vol. 3, 1993; English transl. in Amer. Math. Soc. Transl. Ser. 2, vol. 166, AMS, 1995, pp. 35–100. [Ab3] , A ramification filtration of the Galois group of a local field. II, Proc. Steklov Inst. Math., vol. 208, 1995, pp. 18–69; English transl. in Proc. Steklov Inst. Math., vol. 208. [Ab4] , A ramification filtration of the Galois group of a local field. III, Izv. Ross. Akad. Nauk Ser. Mat. 62 no. 6 (1998), 3–48; English transl. in Izv. Math. 62 (1998), 857–900. [Ab5] , The field of norms functor and the Bruc¨ kner-Vostokov formula, Math. Ann. 308 (1997), 5–19. [Ab6] , Explicit formulas for the Hilbert symbol of a formal group over Witt vectors, Izv. Ross. Akad. Nauk Ser. Mat. 61 no. 3 (1997), 3–56; English transl. in Izv. Math. 61 (1997), 463–515. [Ab7] , A group-theoretic property of ramification filtration, Izv. Ross. Akad. Nauk Ser. Mat. 62 no. 6 (1997), 3–26; English transl. in Izv. Math. 62 (1998), 1073–1094. [Ab8] , On a local analogue of the Grothendieck conjecture, Internat. J. Math 11 (2000), 133–175. [AdCK] E. Arbarello, C. de Concini, V.G. Kac, The infinite wedge representation and the reciprocity law for algebraic curves, Proc. Symp. Pure Math., vol. 49 Part I, 1989, pp. 171–190. [AH1] Emil Artin and H. Hasse, Uber¨ den zweiten Erganzungssatz¨ zum Reziprozitatsg¨ esetz der -ten Potenzreste im Korper¨ der -ten Einheitswurzeln und Oberkorpern¨ von , J. Reine Angew. Math. 154 (1925), 143–148. [AH2] , Die beiden Erganzungssatz¨ zum Reziprzitatsg¨ esetz der -ten Potenzreste im Korper¨ der -ten Einheitswurzeln, Abh. Math. Sem. Univ. Hamburg 6 (1928), 146–162. [Am] Shigeru Amano, Eisenstein equations of degree in a -adic field, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 18 (1971), 1–22. [Ar] Emil Artin, Algebraic numbers and algebraic functions, Gordon and Breach, New York, London, and Paris, 1967. [ASch] Emil Artin and O. Schreier, Eine Kennzeichnung der reell abgeschlossen Korper¨ , Abh. Math. Sem. Univ. Hamburg 5 (1927), 225–231. £¥¤§¦©¨ ¤ © 321 [AT] Emil Artin and John T. Tate, Class field theory. Second Edition, Addison–Wesley, 1990. [AV] David K. Arrowsmith and Franco Vivaldi, Goemetry of -adic Siegel discs, Phys. D. 71 (1994), 222–236. [Ax] James Ax, Zeros of polynomials over local fields, J. Algebra 15 (1970), 417–428. [AxK] James Ax and Simon Kochen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605–630; II, Amer. J. Math. 87 (1965), 631–648; III, Ann. of Math. (2) 83 (1966), 437–456. [Bah] George Bachman, Introduction to -adic numbers and valuation theory, Academic Press, New York and London, 1964. [BaK] T. N. Bailey and A. W. Knapp (eds.), Representation theory and automorphic forms. Proc. Symp. Pure Math., vol. 61, 1997. [Bas] Hyman Bass, Algebraic -theory, Benjamin, New York and Amsterdam, 1968. [Ben1] Denis Benois, Periodes´ -adiques et lois de recipr´ ocite´ explicites, J. Reine Angew. Math. 493 (1997), 115–151. [Ben2] , On Iwasawa theory of cristalline representations, Duke Math. J. 104 (2000), 211–267. [Ber] Vladimir G. Berkovich, Spectral theory and analytic geometry over non-Archimedean fields, Math. Surveys Monogr., vol. 33, AMS, 1990. [BeV1] D. G. Benois and S. V. Vostokov, Norm pairing in formal groups and Galois rep- resentations, Algebra i Analiz 2 (1990), no. 6, 69–97; English transl. in Leningrad Math. J. 2 (1991). [BeV2] D. G. Benois and S. V. Vostokov, Galois representaions in Honda’s formal groups. Arithmetic of the group of points, Tr. St-Peterbg. mat. Obsch., vol. 2, 1993, pp. 3–23; English transl. in Amer. Math. Soc. Transl. Ser. 2, vol. 159, AMS, 1994, pp. 1–14. [BF] Lee Brekke and Peter G. O. Freund, -adic numbers in physics, Phys. Rep. 233 (1993), 1–66. [BGR] S. Bosch, U. Guntzer¨ , and Reinhold Remmert, Non-Archimedean analysis, Grund- lehren Math. Wiss., vol. 261, Springer-Verlag, Berlin and New York, 1984. [BK1] Spencer Bloch and Kazuya Kato, -adic etale cohomology, Inst. Hautes Etudes Sci. Publ. Math. 63 (1986), 107–152. [BK2] Spencer Bloch and Kazuya Kato, ! -functions and Tamagawa numbers of motives, The Grothendieck Festschrift, vol. 1, Birkhauser,¨ 1990, pp. 333–400. [BNW] E. Binz, Jur¨ gen Neukirch, and G. H. Wenzel, A subgroup theorem for free products of pro-finite groups, J. Algebra 19 (1971), 104–109. [Bog] R. A. Bogomolov, Two theorems on divisibility and torsion in the Milnor -groups, Mat. Sb. 130 (1986), no. 3, 404–412; English transl. in Math. USSR-Sb. 58 (1987). [Bor1] Z. I. Borevich, The multiplicative group of cyclic -extensions of a local field, Trudy Mat. Inst. Steklov. 80 (1965), 16–29; English transl. in Proc. Steklov Inst. Math. 1968, no. 80. [Bor2] , Groups of principal units of -extension of a local field, Dokl. Akad. Nauk SSSR 173 (1967), no. 2, 253–255; English transl. in Soviet Math. Dokl. 8 (1967). [Bou] N. Bourbaki, Algebr´ e commutative, Hermann, Paris, 1965. [BoV] Z. I. Borevich and S. V. Vostokov, The ring of integral elements of an extension of prime degree of a local field as a Galois module, Zap. Nauchn. Sem. Leningrad. 322 £¥¤§¦©¨ ¤ © Otdel. Mat. Inst. Steklov (LOMI) 31 (1973), 24–37; English transl. in J. Soviet Math. 6 (1976), no. 3. [Br] R. Brauer, Uber¨ die Konstruktion der Schiefkorper¨ , die von endlichem Rang in bezug auf ein gegebenes Zentrum sind, J. Reine Angew. Math. 168 (1932), 44–64. [Bru1] Helmut Bruckner,¨ Eine explizite Formel zum Reziprozitatsg¨ esetz fur¨ Primzahlexpone- nten , Algebraische Zahlentheorie (Ber. Tag. Math. Forschungsinst. Oberwolfach, 1964), Bibliographisches Institut, Mannheim, 1967, pp. 31–39. [Bru2] , Hilbertsymbole zum Exponenten " und Pfaffische Formen, Preprint, Ham- burg, 1979. [BSh] Z. I. Borevich and I. R. Shafarevich, Number theory, Nauka, Moscow, 1964; English transl., Pure Appl. Math., vol. 20, Academic Press, New York and London, 1966. [BSk] Z. I. Borevich and A. I. Skopin, Extensions of a local field with normal basis for principal units, Trudy Mat. Inst. Steklov. 80 (1965), 45–50; English transl. in Proc. Steklov Inst. Math. 1968, no. 80. [BT] Hyman Bass and John T. Tate, The Milnor ring of a global field, Algebraic -theory, II: “Classical” algebraic -theory and connections with arithmetic (Proc. Conf., Seattle, WA, 1972), Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin, 1973, pp. 349–446. [Bu1] Alexandru Buium, Differential charaters of abelian varieties over -fields, Invent. Math. 122 (1995), 309–340. [Bu2] , Geometry of -jets, Duke Math. J. 82 (1996), 349–367. [Bu3] , Arithmetic analogues of derivations, J. Algebra 198 (1997), 290–299. # [Bu4] , Continuous # -adic functions and -derivations, J. Number Theory 84 (2000), 34–39. [Bu5] , Differential algebraic geometry and Diophantine geometry: an overview, Sympos. Math. 37 (1997), Cambridge Univ. Press, 87–98. [Bum] Daniel Bump, Automorphic forms and representations, Cambridge University Press, 1998. [Bur] D. J. Burns, Factorisability and the arithmetic of wildly ramified Galois extensions, Sem.´ Theor´ . Nombres Bordeaux (2) 1 (1989), 59–65. [Cam] Rachel Camina, Subgroups of the Nottingham group, J. Algebra 196 (1997), 101– 113. [Car] Joseph E. Carroll, On the torsion in 2 of local fields, Algebraic -theory, II: “Classical” algebraic -theory and connections with arithmetic (Proc. Conf., Seat- tle, WA, 1972), Lecture Notes in Math., vol. 342, Springer-Verlag, Berlin, 1973, pp. 464–473. [Cas] J. W. S. Cassels, Local fields, Cambridge Univ. Press, London, 1986. [CF] J. W. S. Cassels and A. Frohlich¨ (eds.), Algebraic number theory, Academic Press, London, and Thompson Book, Washington DC, 1967. [CG] J. Coates, R. Greenberg, Kummer theory for abelian varieties over local fields, Invent. Math. 124 (1996), 129–174. [Ch1] C. Chevalley, Sur la theorie´ du corps de classes dans les corps finis et les corps locaux, J. Fac. Sci. Tokyo Imp. Univ. Ser. Math. 2 (1933), 363–476. [Ch2] , Class field theory, Nagoya University, Nagoya, 1954. [Chr] Gilles Christol, -adic numbers and ultrametricity, From number theory to physics (Les Houches, 1989), Springer, 1992, pp.

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