Chronological table Prerequisites and notations Table of notations PART Ⅰ.ELEMENTARY THEORY Chapter Ⅰ.Locally compact fields 1.Finite fields 2.The module in a locally compact field 3.Classification of locally compact fields 4.Structure of p-fields Chapter Ⅱ.Lattices and duality over local fields 1.Norms 2.Lattices 3.Multiplicative structure of local fields 4.Lattices over R 5.Duality over local fields Chapter Ⅲ.Places of A-fields 1.A-fields and their completions 2.Tensor-products of commutative fields 3.Traces and norms 4.Tensor-products of A-fields and local fields Chapter Ⅳ.Adeles 1.Adeles of A-fields 2.The main theorems 3.Ideles 4.Ideles of A-fields Chapter Ⅴ.Algebraic number-fields 1.Orders in algebras over Q 2.Lattices over algebraic number-fields 3.Ideals 4.Fundamental sets Chapter Ⅵ.The theorem of Riemann-Roch Chapter Ⅶ.Zeta-functions of A-fields 1.Convergence of Euler products 2.Fourier transforms and standard functions 3.Quasicharacters 4.Quasicharacters of A-fields 5.The functional equation 6.The Dedekind zeta-function 7.L-functions 8.The coefficients of the L-series Chapter Ⅷ.Traces and norms 1.Traces and norms in local fields 2.Calculation of the different 3.Ramification theory 4.Traces and norms in A-fields 5.Splitting places in separable extensions 6.An application to inseparable extensions PART Ⅱ.CLASSFIELD THEORY Chapter Ⅸ.Simple algebras 1.Structure of simple algebras
2.The representations of a simple algebra 3.Factor-sets and the Brauer group 4.Cyclic factor-sets 5.Special cyclic factor-sets Chapter Ⅹ.Simple algebras over local fields 1.Orders and lattices 2.Traces and norms 3.Computation of some integrals Chapter ?.Simple algebras over A-fields 1.Ramification 2.The zeta-function of a simple algebra 3.Norms in simple algebras 4.Simple algebras over algebraic number-fields Chapter ?.Local classfield theory 1.The formalism of class field theory 2.The Brauer group of a local field 3.The canonical morphism 4.Ramification of abelian extensions 5.The transfer Chapter ⅩⅢ.Global classfield theory 1.The canonical pairing 2.An elementary lemma 3.Hasse's "law of reciprocity" 4.Classfield theory for Q 5.The Hilbert symbol 6.The Brauer group of an A-field 7.The Hilbert p-symbol 8.The kernel of the canonical morpnism 9.The main theorems 10.Local behavior of abelian extensions 11."Classical" classfield theory 12."Coronidis loco" Notes to the text Appendix Ⅰ.The transfer theorem Appendix Ⅱ.W-groups for local fields Appendix Ⅲ.Shafarevitch's theorem Appendix Ⅳ.The Herbrand distribution Index of definitions
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