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On the structure of the Milnor K–groups of complete discrete valuation fields

Jinya Nakamura

Geometry & Topology Monographs 3 (2000) 123–135

DOI: 10.2140/gtm.2000.3.123

Bibliography
1 S Bloch, Algebraic K–theory and crystalline cohomology, Inst. Hautes Études Sci. Publ. Math. (1977) MR488288
2 S Bloch, K Kato, p–adic étale cohomology, Inst. Hautes Études Sci. Publ. Math. (1986) 107–152 MR849653
3 H Bass, J Tate, The Milnor ring of a global field, from: "Algebraic K–theory, II: “Classical” algebraic K–theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972)", Springer (1973) MR0442061
4 I B Fesenko, Abelian local p–class field theory, Math. Ann. 301 (1995) 561–586 MR1324527
5 J Graham, Continuous symbols on fields of formal power series, from: "Algebraic K–theory, II: “Classical” algebraic K–theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)", Springer (1973) MR0364187
6 L Illusie, Complexe de de Rham–Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. (4) 12 (1979) 501–661 MR565469
7 B Kahn, L'anneau de Milnor d'un corps local à corps résiduel parfait, Ann. Inst. Fourier (Grenoble) 34 (1984) 19–65 MR766273
8 K Kato, A generalization of local class field theory by using K–groups II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980) 603–683 MR603953
9 K Kato, On p–adic vanishing cycles (application of ideas of Fontaine–Messing), from: "Algebraic geometry, Sendai, 1985", Adv. Stud. Pure Math. 10, North-Holland (1987) 207–251 MR946241
10 M Kurihara, Abelian extensions of an absolutely unramified local field with general residue field, Invent. Math. 93 (1988) 451–480 MR948109
11 M Kurihara, The Milnor K–groups of a local ring over a ring of the p–adic integers, from: "Ramification theory for arithmetic schemes, Luminy 1999" (editor B Erez) (to appear)
12 M Kurihara, On the structure of Milnor K–groups of certain complete discrete valuation fields, J. Théor. Nombres Bordeaux 16 (2004) 377–401 MR2143560
13 M Kurihara, A note on p–adic étale cohomology, Proc. Japan Acad. Ser. A Math. Sci. 63 (1987) 275–278 MR931263
14 J Nakamura, On the structures of the Milnor K–groups of some complete discrete valuation fields, K–Theory 19 (2000) 269–309 MR1756261
15 J Nakamura, On the Milnor K–groups of complete discrete valuation fields, Doc. Math. 5 (2000) 151–200 MR1756354
16 A N Parshin, Local class field theory, Trudy Mat. Inst. Steklov. 165 (1984) 143–170 MR752939 Algebraic geometry and its applications
17 I Zhukov, Milnor and topological K–groups of higher-dimensional complete fields, Algebra i Analiz 9 (1997) 98–147 MR1458420