I. Cohomology of profinite groups.- ???1. Profinite groups.- 1.1 Definition.- 1.2 Subgroups.- 1.3 Indices.- 1.4 Pro-p-groups and Sylow p-subgroups.- 1.5 Pro-p-groups.- ???2. Cohomology.- 2.1 Discrete G-modules.- 2.2 Cochains, cocycles, cohomology.- 2.3 Low dimensions.- 2.4 Fimctoriality.- 2.5 Induced modules.- 2.6 Complements.- ???3. Cohomological dimension.- 3.1 p-cohomological dimension.- 3.2 Strict cohomological dimension.- 3.3 Cohomological dimension of subgroups and extensions.- 3.4 Characterization of the profinite ...
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I. Cohomology of profinite groups.- ???1. Profinite groups.- 1.1 Definition.- 1.2 Subgroups.- 1.3 Indices.- 1.4 Pro-p-groups and Sylow p-subgroups.- 1.5 Pro-p-groups.- ???2. Cohomology.- 2.1 Discrete G-modules.- 2.2 Cochains, cocycles, cohomology.- 2.3 Low dimensions.- 2.4 Fimctoriality.- 2.5 Induced modules.- 2.6 Complements.- ???3. Cohomological dimension.- 3.1 p-cohomological dimension.- 3.2 Strict cohomological dimension.- 3.3 Cohomological dimension of subgroups and extensions.- 3.4 Characterization of the profinite groups G such that cdp(G) ? 1.- 3.5 Dualizing modules.- ???4. Cohomology of pro-p-groups.- 4.1 Simple modules.- 4.2 Interpretation of H1: generators.- 4.3 Interpretation of H2: relations.- 4.4 A theorem of Shafarevich.- 4.5 Poincar??? groups.- ???5. Nonabelian cohomology.- 5.1 Definition of H0 and of H1.- 5.2 Principal homogeneous spaces over A - a new definition of H1(G, A).- 5.3 Twisting.- 5.4 The cohomology exact sequence associated to a subgroup.- 5.5 Cohomology exact sequence associated to a normal subgroup.- 5.6 The case of an abelian normal subgroup.- 5.7 The case of a central subgroup.- 5.8 Complements.- 5.9 A property of groups with cohomological dimension ? 1.- II. Galois cohomology, the commutative case.- ???1. Generalities.- 1.1 Galois cohomology.- 1.2 First examples.- ???2. Criteria for cohomological dimension.- 2.1 An auxiliary result.- 2.2 Case when p is equal to the characteristic.- 2.3 Case when p differs from the characteristic.- ???3. Fields of dimension ?1.- 3.1 Definition.- 3.2 Relation with the property (C1).- 3.3 Examples of fields of dimension ? 1.- ???4. Transition theorems.- 4.1 Algebraic extensions.- 4.2 Transcendental extensions.- 4.3 Local fields.- 4.4 Cohomological dimension of the Galois group of an algebraic number field.- 4.5 Property (Cr).- ???5. p-adic fields.- 5.1 Summary of known results.- 5.2 Cohomology of finite Gk-modules.- 5.3 First applications.- 5.4 The Euler-Poincar??? characteristic (elementary case).- 5.5 Unramified cohomology.- 5.6 The Galois group of the maximal p-extension of k.- 5.7 Euler-Poincar??? characteristics.- 5.8 Groups of multiplicative type.- ???6. Algebraic number fields.- 6.1 Finite modules - definition of the groups Pi(k, A).- 6.2 The finiteness theorem.- 6.3 Statements of the theorems of Poitou and Tate.- III. Nonabelian Galois cohomology.- ???1. Forms.- 1.1 Tensors.- 1.2 Examples.- 1.3 Varieties, algebraic groups, etc.- 1.4 Example: the k-forms of the group SLn.- ???2. Fields of dimension ? 1.- 2.1 Linear groups: summary of known results.- 2.2 Vanishing of H1 for connected linear groups.- 2.3 Steinberg's theorem.- 2.4 Rational points on homogeneous spaces.- ???3. Fields of dimension ? 2.- 3.1 Conjecture II.- 3.2 Examples.- ???4. Finiteness theorems.- 4.1 Condition (F).- 4.2 Fields of type (F).- 4.3 Finiteness of the cohomology of linear groups.- 4.4 Finiteness of orbits.- 4.5 The case k = R.- 4.6 Algebraic number fields (Borel's theorem).- 4.7 A counter-example to the "Hasse principle".
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New in new dust jacket. Sewn binding. Cloth over boards. 212 p. Contains: Illustrations, black & white. Eso Astrophysics Symposia. Audience: General/trade. Please double check the textbook description: Express shipping takes 3-5 days with free tracking number! Brand New Paperback International edition textbook, 1st edition. Different ISBN number and book cover design. The content is exactly same as original US edition. The book printed in Black/White, the book cover may contain the foreign words and the restriction sale disclaimer.
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New in new dust jacket. Sewn binding. Cloth over boards. 212 p. Contains: Illustrations, black & white. Eso Astrophysics Symposia. Audience: General/trade. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.
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Near Fine. Corrected second printing (2002) of the first English edition (1997). Crisp, clean pages with no owners' marks; the hard cover shows only minor softening at the spine heel, otherwise excellent. x, 210pp. incl. index.; Springer Monographs in Mathematics Series.
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New in new dust jacket. Trade paperback (US). Glued binding. 212 p. Contains: Illustrations, black & white. Springer Monographs in Mathematics. Audience: General/trade. Please double check the textbook description: Express shipping takes 3-5 days with free tracking number! Brand New Paperback International edition textbook, 1st edition. Different ISBN number and book cover design. The content is exactly same as original US edition. The book printed in Black/White, the book cover may contain the foreign words and the restriction sale disclaimer.
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New in new dust jacket. Trade paperback (US). Glued binding. 212 p. Contains: Illustrations, black & white. Springer Monographs in Mathematics. Audience: General/trade. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service.
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New. Sewn binding. Cloth over boards. 212 p. Springer Monographs in Mathematics. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Fine. Sewn binding. Cloth over boards. 212 p. Springer Monographs in Mathematics. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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New. Trade paperback (US). Glued binding. 212 p. Springer Monographs in Mathematics. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
