LEADER 04419nam 2200589 450 001 9910788780103321 005 20170821165756.0 010 $a0-8218-7601-5 035 $a(CKB)3240000000069540 035 $a(EBL)3112904 035 $a(SSID)ssj0000629223 035 $a(PQKBManifestationID)11398656 035 $a(PQKBTitleCode)TC0000629223 035 $a(PQKBWorkID)10718723 035 $a(PQKB)10493621 035 $a(MiAaPQ)EBC3112904 035 $a(RPAM)3751845 035 $a(PPN)197103332 035 $a(EXLCZ)993240000000069540 100 $a20140523h19831983 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced analytic number theory$hPart 1$iRamification theoretic methods /$fCarlos J. Moreno 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[1983] 210 4$dİ1983 215 $a1 online resource (202 p.) 225 1 $aContemporary mathematics,$x0271-4132 ;$v15 300 $aDescription based upon print version of record. 311 $a0-8218-5015-6 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Preface""; ""Chapter 0. Introduction""; ""A?1. A historical perspective""; ""A?2. The explicit formulas: motivation""; ""Chapter I. Galois Theory for Infinite Extensions""; ""A?1. Fundamental Theorem of Galois Theory for infinite extensions""; ""A?2. Topological properties of Gal(K'/K)""; ""A?3. Example""; ""Chapter II. Projective Limits""; ""A?1. Basic definitions""; ""A?2. Examples""; ""A?3. Homomorphisms""; ""Chapter III. Elementary Theory of l-adic Integration""; ""A?1. Distributions and measures""; ""A?2. Measures on groups""; ""A?3. Riemann sums"" 327 $a""A?4. l-adic Haar measures""""A?5. Examples""; ""Chapter IV. Ramification Theory""; ""A?1. The v-function""; ""A?2. Transitivity properties of the v-function""; ""A?3. The different""; ""A?4. Transitivity properties of the different""; ""A?5. Complementary basis""; ""A?6. Fundamental inequality and the C-invariant""; ""A?7. Quotients of Galois groups and Herbrand's Theorem""; ""Chapter V. Multiplicative versus Additive Reduction""; ""A?1. The case of a local field""; ""A?2. The module structure of the unit group""; ""A?3. The case of an elliptic curve"" 327 $a""Chapter VI. Ramification of Abelian Extensions""""A?1. Index computations""; ""A?2. Main Theorem""; ""Chapter VII. The Weil Groups of a Local Field""; ""A?1. The Frobenius automorphism""; ""A?2. The relative Weil group of a non-archimedean local field""; ""A?3. The absolute Weil group""; ""A?4. The Weil group of an archimedean local field""; ""A?5. The Weil-Deligne group""; ""Appendix: The non-abelian local reciprocity law""; ""Chapter VIII. Shafarevitch's Theorem""; ""A?1. Representations of a simple algebra""; ""A?2. Factor sets""; ""A?3. Subalgebras of central simple algebras"" 327 $a""A?4. Cyclic algebras""""A?5. Algebras and group extensions""; ""A?6. Powers of central simple algebras""; ""A?7. Generators of the Brauer group""; ""A?8. Structure of the relative Weil group""; ""A?9. Shafarevitch's Theorem""; ""Appendix: I. The Brauer group of central 'simple algebras over K""; ""II. The group H2(G,Kxs)""; ""Chapter IX. The Herbrand Distribution""; ""A?1. The Herbrand distribution: definition and basic facts""; ""A?2. The support of the Herbrand distribution""; ""A?3. Determination of the Herbrand distribution on Gal(Kab/K)"" 327 $a""A?4. Functoriality properties of the Herbrand distribution""""A?5. The Herbrand distribution and measures on the Weil group""; ""A?6. The integral formula for the Herbrand distribution""; ""A?7. Conductors, the Artin representation, and the Herbrand distribution""; ""Bibliography""; ""Index""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""P""; ""R""; ""S""; ""T""; ""w"" 410 0$aContemporary mathematics (American Mathematical Society) ;$v15. 606 $aNumber theory 606 $aAlgebraic fields 615 0$aNumber theory. 615 0$aAlgebraic fields. 676 $a512/.7 700 $aMoreno$b Carlos J.$057537 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788780103321 996 $aAdvanced analytic number theory$9381823 997 $aUNINA