The explicit reciprocity law and the cohomology of Fontaine-Messing

DOI10.24033/bsmf.2173zbMath0752.14015OpenAlexW1483834401MaRDI QIDQ3986553

Kazuya Kato

Publication date: 27 June 1992

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1991__119_4_397_0

zbMATH Keywords

reciprocity lawregular local ringsMilnor \(K\)-groupssymbol mapsFontaine-Messing cohomology

Mathematics Subject Classification ID

(p)-adic cohomology, crystalline cohomology (14F30) Regular local rings (13H05) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

Related Items

A finer Tate duality theorem for local Galois symbols, An analogue of the field-of-norms functor and of the Grothendieck conjecture, Differential characters of abelian varieties over \(p\)-adic fields, The Brückner-Vostokov formula for the Hilbert symbol and its validity in the case \(p=2\), Abelian extensions of an absolutely unramified local field with general residue field, Syntomic regulators and values of \(p\)-adic \(L\)-functions. I. Appendix by Masato Kurihara, On the properties of the Vostokov and Parshin pairing in higher local class field theory, Logarithmic \(p\)-bases and arithmetical differential modules, Crystalline $$\mathbb {Z}_p$$-Representations and $$A_{\inf }$$-Representations with Frobenius, The field-of-norms functor and the Hilbert symbol for higher local fields, Cycle classes in overconvergent rigid cohomology and a semistable Lefschetz theorem, On the $p$ adic nearby cycles of log smooth families, Formal Chow groups, \(p\)-divisible groups and syntomic cohomology., On the structure of Milnor \(K\)-groups of certain complete discrete valuation fields, p-adic étale Tate twists and arithmetic duality☆, The theory of Coleman power series for 𝐾₂, Generalization of the Artin-Hasse logarithm for the Milnor -groups of -rings, Syntomic cohomology and Beilinson’s Tate conjecture for 𝐾₂, On Iwasawa theory of crystalline representations, Appendix: On a theorem of Bloch and Kato (letter to B. Perrin- Riou)

Cites Work

• Les suites spectrales associées au complexe de De Rham-Witt
• Norm pairing in a two-dimensional local field
• Torsion dans le groupe de Chow de codimension deux
• \(p\)-adic étale cohomology
• Note on the Kummer-Hilbert reciprocity law
• Hilbert symbol in a discrete valuated field
• Higher explicit reciprocity laws
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
• Anneaux locaux henséliens
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• On explicit formulas for the norm residue symbol
• Opérations En K-Théorie Algébrique
• EXPLICIT CONSTRUCTION OF CLASS FIELD THEORY FOR A MULTIDIMENSIONAL LOCAL FIELD
• Complexe de de\thinspace Rham-Witt et cohomologie cristalline
• EXPLICIT FORM OF THE LAW OF RECIPROCITY
• The dilogarithm and the norm residue symbol
• Notes on Crystalline Cohomology. (MN-21)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item