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Etale cohomology theory /

Fu, Lei.

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Etale cohomology theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Etale cohomology theory // Lei Fu.
作者:	Fu, Lei.
出版者:	Singapore ;World Scientific, : c2011.,
面頁冊數:	ix, 611 p. ;24 cm.
內容註:	Machine generated contents note: 1.Descent Theory -- 1.1.Flat Modules -- 1.2.Faithfully Flat Modules -- 1.3.Local Criteria for Flatness -- 1.4.Constructible Sets -- 1.5.Flat Morphisms -- 1.6.Descent of Quasi-coherent Sheaves -- 1.7.Descent of Properties of Morphisms -- 1.8.Descent of Schemes -- 1.9.Quasi-finite Morphisms -- 1.10.Passage to Limit -- 2.Etale Morphisms and Smooth Morphisms -- 2.1.The Sheaf of Relative Differentials -- 2.2.Unramified Morphisms -- 2.3.Etale Morphisms -- 2.4.Smooth Morphisms -- 2.5.Jacobian Criterion -- 2.6.Infinitesimal Liftings of Morphisms -- 2.7.Direct Limits and Inverse Limits -- 2.8.Henselization -- 2.9.Etale Morphisms between Normal Schemes -- 3.Etale Fundamental Groups -- 3.1.Finite Group Actions on Schemes -- 3.2.Etale Covering Spaces and Fundamental Groups -- 3.3.Functorial Properties of Fundamental Groups -- 4.Group Cohomology and Galois Cohomology -- 4.1.Group Cohomology -- 4.2.Profinite Groups -- 4.3.Cohomology of Profinite Groups -- 4.4.Cohomological Dimensions -- 4.5.Galois Cohomology -- 5.Etale Cohomology -- 5.1.Presheavcs and Cech Cohomology -- 5.2.Etale Sheaves -- 5.3.Stalks of Sheaves -- 5.4.Recollement of Sheaves -- 5.5.The Functor f! -- 5.6.Etale Cohomology -- 5.7.Calculation of Etale Cohomology -- 5.8.Constructible Sheaves -- 5.9.Passage to Limit -- 6.Derived Categories and Derived Functors -- 6.1.Triangulated Categories -- 6.2.Derived Categories -- 6.3.Derived Functors -- 6.4.RHom(-,-) and -- ��-- 6.5.Way-out Functors -- 7.Base Change Theorems -- 7.1.Divisors -- 7.2.Cohomology of Curves -- 7.3.Proper Base Change Theorem -- 7.4.Cohomology with Proper Support -- 7.5.Cohomological Dimension of Rf -- 7.6.Local Acyclicity -- 7.7.Smooth Base Change Theorem -- 7.8.Finiteness of Rf! -- 8.Duality -- 8.1.Extensions of Henselian Discrete Valuation Rings -- 8.2.Trace Morphisms -- 8.3.Duality for Curves -- 8.4.The Functor Rf! -- 8.5.Poincare Duality -- 8.6.Cohomology Classes of Algebraic Cycles -- 9.Finiteness Theorems -- 9.1.Sheaves with Group Actions -- 9.2.Nearby Cycle and Vanishing Cycle -- 9.3.Generic Base Change Theorem and Generic Local Acyclicity -- 9.4.Finiteness of R峔庢 -- 9.5.Finiteness Theorems -- 9.6.Biduality -- 10.l-adic Cohomology -- 10.1.Adic Formalism -- 10.2.Grothendieck-Ogg-Shafarevich Formula -- 10.3.Frobenius Correspondences -- 10.4.Lefschetz Trace Formula -- 10.5.Grothendieck's Formula of L-functions.
標題:	Homology theory. -
ISBN:	9789814307727 (hbk.) :

Etale cohomology theory /
Fu, Lei.

Etale cohomology theory /Lei Fu. - Singapore ;World Scientific,c2011. - ix, 611 p. ;24 cm. - Nankai tracts in mathematics ;v. 13. - Nankai tracts in mathematics ;v. 13..

Includes bibliographical references (p. 607-608) and index.

Machine generated contents note: 1.Descent Theory -- 1.1.Flat Modules -- 1.2.Faithfully Flat Modules -- 1.3.Local Criteria for Flatness -- 1.4.Constructible Sets -- 1.5.Flat Morphisms -- 1.6.Descent of Quasi-coherent Sheaves -- 1.7.Descent of Properties of Morphisms -- 1.8.Descent of Schemes -- 1.9.Quasi-finite Morphisms -- 1.10.Passage to Limit -- 2.Etale Morphisms and Smooth Morphisms -- 2.1.The Sheaf of Relative Differentials -- 2.2.Unramified Morphisms -- 2.3.Etale Morphisms -- 2.4.Smooth Morphisms -- 2.5.Jacobian Criterion -- 2.6.Infinitesimal Liftings of Morphisms -- 2.7.Direct Limits and Inverse Limits -- 2.8.Henselization -- 2.9.Etale Morphisms between Normal Schemes -- 3.Etale Fundamental Groups -- 3.1.Finite Group Actions on Schemes -- 3.2.Etale Covering Spaces and Fundamental Groups -- 3.3.Functorial Properties of Fundamental Groups -- 4.Group Cohomology and Galois Cohomology -- 4.1.Group Cohomology -- 4.2.Profinite Groups -- 4.3.Cohomology of Profinite Groups -- 4.4.Cohomological Dimensions -- 4.5.Galois Cohomology -- 5.Etale Cohomology -- 5.1.Presheavcs and Cech Cohomology -- 5.2.Etale Sheaves -- 5.3.Stalks of Sheaves -- 5.4.Recollement of Sheaves -- 5.5.The Functor f! -- 5.6.Etale Cohomology -- 5.7.Calculation of Etale Cohomology -- 5.8.Constructible Sheaves -- 5.9.Passage to Limit -- 6.Derived Categories and Derived Functors -- 6.1.Triangulated Categories -- 6.2.Derived Categories -- 6.3.Derived Functors -- 6.4.RHom(-,-) and -- ��-- 6.5.Way-out Functors -- 7.Base Change Theorems -- 7.1.Divisors -- 7.2.Cohomology of Curves -- 7.3.Proper Base Change Theorem -- 7.4.Cohomology with Proper Support -- 7.5.Cohomological Dimension of Rf -- 7.6.Local Acyclicity -- 7.7.Smooth Base Change Theorem -- 7.8.Finiteness of Rf! -- 8.Duality -- 8.1.Extensions of Henselian Discrete Valuation Rings -- 8.2.Trace Morphisms -- 8.3.Duality for Curves -- 8.4.The Functor Rf! -- 8.5.Poincare Duality -- 8.6.Cohomology Classes of Algebraic Cycles -- 9.Finiteness Theorems -- 9.1.Sheaves with Group Actions -- 9.2.Nearby Cycle and Vanishing Cycle -- 9.3.Generic Base Change Theorem and Generic Local Acyclicity -- 9.4.Finiteness of R峔庢 -- 9.5.Finiteness Theorems -- 9.6.Biduality -- 10.l-adic Cohomology -- 10.1.Adic Formalism -- 10.2.Grothendieck-Ogg-Shafarevich Formula -- 10.3.Frobenius Correspondences -- 10.4.Lefschetz Trace Formula -- 10.5.Grothendieck's Formula of L-functions.

ISBN: 9789814307727 (hbk.) :US153.00Subjects--Topical Terms:

555733
Homology theory.

Dewey Class. No.: 514.23

Etale cohomology theory /
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035 $a (OCoLC)587124404
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100 1 $a Fu, Lei. $3 736373
245 1 0 $a Etale cohomology theory / $c Lei Fu.
260 # $a Singapore ; $a Hackensack, N.J. : $b World Scientific, $c c2011.
300 $a ix, 611 p. ; $c 24 cm.
490 1 $a Nankai tracts in mathematics ; $v v. 13
504 $a Includes bibliographical references (p. 607-608) and index.
505 0 # $a Machine generated contents note: 1.Descent Theory -- 1.1.Flat Modules -- 1.2.Faithfully Flat Modules -- 1.3.Local Criteria for Flatness -- 1.4.Constructible Sets -- 1.5.Flat Morphisms -- 1.6.Descent of Quasi-coherent Sheaves -- 1.7.Descent of Properties of Morphisms -- 1.8.Descent of Schemes -- 1.9.Quasi-finite Morphisms -- 1.10.Passage to Limit -- 2.Etale Morphisms and Smooth Morphisms -- 2.1.The Sheaf of Relative Differentials -- 2.2.Unramified Morphisms -- 2.3.Etale Morphisms -- 2.4.Smooth Morphisms -- 2.5.Jacobian Criterion -- 2.6.Infinitesimal Liftings of Morphisms -- 2.7.Direct Limits and Inverse Limits -- 2.8.Henselization -- 2.9.Etale Morphisms between Normal Schemes -- 3.Etale Fundamental Groups -- 3.1.Finite Group Actions on Schemes -- 3.2.Etale Covering Spaces and Fundamental Groups -- 3.3.Functorial Properties of Fundamental Groups -- 4.Group Cohomology and Galois Cohomology -- 4.1.Group Cohomology -- 4.2.Profinite Groups -- 4.3.Cohomology of Profinite Groups -- 4.4.Cohomological Dimensions -- 4.5.Galois Cohomology -- 5.Etale Cohomology -- 5.1.Presheavcs and Cech Cohomology -- 5.2.Etale Sheaves -- 5.3.Stalks of Sheaves -- 5.4.Recollement of Sheaves -- 5.5.The Functor f! -- 5.6.Etale Cohomology -- 5.7.Calculation of Etale Cohomology -- 5.8.Constructible Sheaves -- 5.9.Passage to Limit -- 6.Derived Categories and Derived Functors -- 6.1.Triangulated Categories -- 6.2.Derived Categories -- 6.3.Derived Functors -- 6.4.RHom(-,-) and -- ��-- 6.5.Way-out Functors -- 7.Base Change Theorems -- 7.1.Divisors -- 7.2.Cohomology of Curves -- 7.3.Proper Base Change Theorem -- 7.4.Cohomology with Proper Support -- 7.5.Cohomological Dimension of Rf -- 7.6.Local Acyclicity -- 7.7.Smooth Base Change Theorem -- 7.8.Finiteness of Rf! -- 8.Duality -- 8.1.Extensions of Henselian Discrete Valuation Rings -- 8.2.Trace Morphisms -- 8.3.Duality for Curves -- 8.4.The Functor Rf! -- 8.5.Poincare Duality -- 8.6.Cohomology Classes of Algebraic Cycles -- 9.Finiteness Theorems -- 9.1.Sheaves with Group Actions -- 9.2.Nearby Cycle and Vanishing Cycle -- 9.3.Generic Base Change Theorem and Generic Local Acyclicity -- 9.4.Finiteness of R峔庢 -- 9.5.Finiteness Theorems -- 9.6.Biduality -- 10.l-adic Cohomology -- 10.1.Adic Formalism -- 10.2.Grothendieck-Ogg-Shafarevich Formula -- 10.3.Frobenius Correspondences -- 10.4.Lefschetz Trace Formula -- 10.5.Grothendieck's Formula of L-functions.
650 # 0 $a Homology theory. $3 555733
830 0 $a Nankai tracts in mathematics ; $v v. 13. $3 1306051