The explicit reciprocity law and the cohomology of Fontaine-Messing

 Access to full text

 Full (PDF)

1. [AH] ARTIN (E.) and HASSE (H.). — Die beiden Ergänzungssätze zum Reziprozitätsgesetze der ln-ten Potenzreste im Körper der ln-ten Einheiten Wurseln, Abh. Math. Sem. Univ. Hambourg, t. 6, 1928, p. 146-162. Zbl54.0191.05JFM54.0191.05
2. [BO] BERTHELOT (P.) and OGUS (A.). — Notes on crystalline cohomology, Princeton University Press, 1978. Zbl0383.14010MR58 #10908
3. [BK] BLOCH (S.) and KATO (K.). — p-adic etale cohomology, Inst. Hautes Études Sci. Publ. Math., t. 63, 1986, p. 107-152. Zbl0613.14017MR87k:14018
4. [B1] BRÜCKNER (H.). — Hilbertsymbole zum Exponenten pn und Pfaffsche Formen. — Preprint, Hamburg, 1979. 
5. [B2] BRÜCKNER (H.). — Explizites reziprozitätsgesetz und anwendungen. — Vorlesungen aus dem Fachbereich Mathematik der Universität Essen, 1979. Zbl0415.12004
6. [C] COLEMAN (R.F.). — The dilogarithm and the norm residue symbol, Bull. Soc. Math. France, t. 109, 1981, p. 373-402. Zbl0493.12019MR84j:12017
7. [CSS] COLLIOT THÉLÈNE (J.-L.), SANSUC (J.-J.) and SOULÉ (C.). — Torsion dans le goupe de Chow de codimension deux, Duke Math. J., t. 50, 1983, p. 763-801. Zbl0574.14004
8. [FM] FONTAINE (J.-M.) and MESSING (W.). — Contemporary Math., t. 67, 1987, p. 179-207. Zbl0632.14016MR89g:14009
9. [Gr] GROTHENDIECK (A.). — Éléments de Géométrie algébrique, IV, première partie, Inst. Hautes Études Sci. Publ. Math., t. 20, 1964. Zbl0136.15901
10. [Gu] GUIN (D.). — Stabilité de l'homologie du groupe linéaire et K-théorie algébrique, C.R. Acad. Sci. Paris Sér. I, Math., t. 304, 9, 1987, p. 219-222. Zbl0609.18005MR88f:18015
11. [H] HARTSHORNE (R.). — Residues and Duality, in Lecture Notes in Math., 20, Springer, 1966. Zbl0212.26101MR36 #5145
12. [I1] ILLUSIE (L.). — Complexe de de Rham-Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup., t. 12, 1979, p. 501-661. Zbl0436.14007MR82d:14013
13. [IR] ILLUSIE (L.) and RAYNAUD (M.). — Les suites spectrales associées au complexe de de Rham-Witt, Inst. Hautes Études Sci. Publ. Math., t. 57, 1983, p. 73-212. Zbl0538.14012MR85e:14026
14. [Iw] IWASAWA (K.). — On explicit formulas for the norm residue symbol, J. Math. Soc. Japan, t. 20, 1968, p. 151-165. Zbl0256.12013MR37 #5183
15. [K1] KATO (K.). — A generalization of local class field theory by using K-groups, II, J. Fac. Sci. Univ. Tokyo Sect. IA Math., t. 27, 1980, p. 602-683. Zbl0463.12006MR83g:12020a
16. [K2] KATO (K.). — A generalization of local class field theory by using K-groups, III, J. Fac. Sci. Univ. Tokyo Sect. IA Math., t. 29, 1982, p. 31-43. Zbl0503.12004MR83g:12020b
17. [K3] KATO (K.). — Galois cohomology of complete discrete valuation fields, in Lecture Notes in Math., 967, Springer, 1982. Zbl0506.12022MR84k:12006
18. [K4] KATO (K.). — Duality theories in p-primary etale cohomology, I, Algebraic and topological theories, Kinokuniya, 1985, p. 127-148. Zbl0800.14009MR1102256
19. [K5] KATO (K.). — On p-adic vanishing cycles, Preprint, Springer, 1985. 
20. [R] RAYNAUD (M.). — Anneaux locaux henséliens, Lecture Notes in Math., 169, Springer, 1970. Zbl0203.05102MR43 #3252
21. [Sa] SAFAREVIC (I.R.). — A general reciprocity law, Mat. Sb., t. 26, 68, 1950, p. 113-146. Zbl0036.15901MR11,230f
22. [Sh] SHIRATANI (K.). — Notes on the Kummer-Hilbert reciprocity law, J. Math. Soc. Japan, t. 12, 1960, p. 412-421. Zbl0111.04502MR24 #A2575
23. [So] SOULÉ (C.). — Opérations en K-théorie Algébrique, Canadian J. Math., t. 37, 1985, p. 488-550. Zbl0575.14015MR87b:18013
24. [S1] SUSLIN (A.A.). — Mennicke symbols and their applications in the K-theory of fields, in Lecture Notes in Math., 966, Springer, 1982. Zbl0502.18004MR84f:18023
25. [S2] SUSLIN (A.A.). — Homology of GLn, characteristic classes and Milnor K-theory, in Lecture Notes in Math., 1046, Springer, 1984, p. 357-375. Zbl0528.18007MR86f:11090a
26. [V1] VOSTOKOV (S.V.). — Explicit form of the law of reciprocity, Izv. Akad. Nauk SSSR Ser. Mat., t. 13, 1979, p. 557-588. Zbl0467.12018
27. [V2] VOSTOKOV (S.V.). — Hilbert symbols in a discrete valuated field, J. Sov. Math., t. 19, 1, 1982, p. 1006-1019. Zbl0486.12007
28. [V3] VOSTOKOV (S.V.). — Explicit construction of class field theory for a multidimensional local field, Izv. Akad. Nauk SSSR Ser. Mat., t. 26, 1986, p. 263-287. Zbl0608.12017
29. [VK] VOSTOKOV (S.V.) and KIRILLOV (A.N.). — Normed pairing in a two dimensional local field, J. Sov. Math., t. 30, 1, 1985, p. 1847-1853. Zbl0566.12006
30. [W] WILES (A.). — Higher explicit reciprocity laws, Ann. of Math., t. 107, 1978, p. 235-254. Zbl0378.12006MR58 #605
31. 1) The contents of § 1 are treated in the paper : BERTHELOT (P.) and MESSING (W.). — Théorie de Dieudonné cristalline III, The Grothendieck Festschrift, vol. III, Birkhäuser 1990, p. 173-247. Zbl0753.14041MR92h:14012
32. 2) The modified complex S′n(r)A,B in § 3 is related to the crystalline cohomology theory with logarithmic poles developped in the following papers : FALTINGS (G.). — F-isocrystals on open varieties : Results and Conjectures, The Grothendieck Festschrift, vol. II, Birkhäuser 1990, p. 219-248. Zbl0736.14004MR92f:14015
33. KATO (K.). — Logarithmic structures of Fontaine-Illusie, Proc. of first JAMI conference, John Hopkins Univ. Press, 1990, p. 80-99. 

1. Victor Abrashkin, Ruth Jenni, The field-of-norms functor and the Hilbert symbol for higher local fields
2. Takeshi Tsuji, On the $p$ adic nearby cycles of log smooth families
3. Masato Kurihara, On the structure of Milnor $K$-groups of certain complete discrete valuation fields
4. Kanetomo Sato, p-adic étale Tate twists and arithmetic duality
5. Pierre Colmez, La conjecture de Birch et Swinnerton-Dyer $𝐩$-adique