Profinite Groups, Arithmetic, and GeometryPrinceton University Press, 1972年3月21日 - 252 頁 In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations. |
內容
PREFACE vii | 3 |
COHOMOLOGY OF PROFINITE GROUPS | 16 |
COHOMOLOGICAL DIMENSION | 53 |
GALOIS COHOMOLOGY AND FIELD THEORY | 93 |
CHAPTER V LOCAL CLASS FIELD THEORY | 129 |
CHAPTER VI DUALITY | 183 |
| 248 | |
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常見字詞
abelian group algebraic assume Br(k Brauer group cdp G Čech class field theory cocycle coefficients cohomological dimension cohomologically trivial cohomology groups cohomology sequence commutative diagram compact cup-product d-functor deduce defined denote dual duality element étale exact sequence exists extension K/k finite extension finite group finite group scheme follows functor G-module Galois group given group G group scheme H¹(A H¹(G H¹(k H²(G hence homomorphism induced injective integer isomorphism kernel Lemma Let G Let K/k Moreover morphism multiplicative non-trivial zero norm normal subgroup obtain open subgroup p-group p-power p-Sylow subgroup pairing Poincaré group presheaf prime number prime-to-p profinite group proj lim prove Q.E.D. COROLLARY Q.E.D. PROPOSITION reciprocity law residue field sheaf shows Spec spectral sequence subgroup of G surjective Theorem topology torsion unramified unramified extension vanishes variables yields Z/pZ