LEADER 03509nam 22004695 450 001 996418191603316 005 20200629203320.0 010 $a3-030-43901-1 024 7 $a10.1007/978-3-030-43901-9 035 $a(CKB)5310000000016664 035 $a(MiAaPQ)EBC6235527 035 $a(DE-He213)978-3-030-43901-9 035 $a(PPN)248595776 035 $a(EXLCZ)995310000000016664 100 $a20200623d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGalois Cohomology and Class Field Theory$b[electronic resource] /$fby David Harari 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (xiv, 338 pages) 225 1 $aUniversitext,$x0172-5939 311 $a3-030-43900-3 327 $aPreface -- Part I Group cohomology and Galois cohomology: generalities -- 1 Cohomology of finite groups -- 2 Cohomology of cyclic groups -- 3 p-groups, the Tate-Nakayama theorem -- 4 Cohomology of profinite groups -- 5 Cohomological dimension -- 6 First notions of Galois cohomology -- Part II Local fields -- 7 Basic facts about local fields -- 8 Brauer group of a local field -- 9 Local class field theory: the reciprocity law -- 10 The Tate local duality theorem -- 11 Local class field theory: Lubin-Tate theory -- Part III Global fields -- 12 Basic facts about global fields -- 13 Cohomology of the idèles -- 14 Reciprocity law -- 15 The abelianized absolute Galois group of a global field -- Part IV Duality theorems -- 16 Class formations -- 17 Poitou-Tate duality -- 18 Some applications -- Appendix -- A Some results from homological algebra -- B A survey of analytic methods -- References -- Index. 330 $aThis graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the ?ebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference. 410 0$aUniversitext,$x0172-5939 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512.32 700 $aHarari$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$01015187 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418191603316 996 $aGalois Cohomology and Class Field Theory$92369392 997 $aUNISA