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"This volume presents for the first time complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry....Will be of great interest to many mathematicians."
--SCI-TECH BOOK NEWS --This text refers to an out of print or unavailable edition of this title.
--SCI-TECH BOOK NEWS --This text refers to an out of print or unavailable edition of this title.
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This volume presents for the first time complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. Chapter 1 is devoted to an exposition of these theorems in the Galois cohomology of number fields announced by Tate in 1962 and describes later work in the same area. The discussion assumes only a knowledge of basic Galois cohomology and class field theory.
Chapter 2 focuses on the work of Artin and Verdier who re-interpreted and developed Tate's ideas in the framework of etale cohomology; some of the more recent developments in this area are also covered.
Finally, in Chapter 3, which contains a number of new results, it is shown how flat cohomology is needed in order to prove and to apply duality theorems in the case of groups which have torsion of order divisible by one of the residue characteristics. --This text refers to an out of print or unavailable edition of this title.
Chapter 2 focuses on the work of Artin and Verdier who re-interpreted and developed Tate's ideas in the framework of etale cohomology; some of the more recent developments in this area are also covered.
Finally, in Chapter 3, which contains a number of new results, it is shown how flat cohomology is needed in order to prove and to apply duality theorems in the case of groups which have torsion of order divisible by one of the residue characteristics. --This text refers to an out of print or unavailable edition of this title.
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composition series whose quotients, exact annihilators, finite flat group scheme, étale group scheme, canonical nondegenerate pairing, locally constant constructible sheaf, smooth group scheme, finite group schemes, flat cohomology, flat group schemes, algebraic group schemes, complete smooth curve, lower pairing, archimedean primes, discriminant ideal, preserves injectives, reciprocity map, number field case, whose generic fibre, abelian scheme, exact commutative diagram, semistable reduction, function field case, cohomology sequence, constructible sheaves New!
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composition series whose quotients, exact annihilators, finite flat group scheme, étale group scheme, canonical nondegenerate pairing, locally constant constructible sheaf, smooth group scheme, finite group schemes, flat cohomology, flat group schemes, algebraic group schemes, complete smooth curve, lower pairing, archimedean primes, discriminant ideal, preserves injectives, reciprocity map, number field case, whose generic fibre, abelian scheme, exact commutative diagram, semistable reduction, function field case, cohomology sequence, constructible sheaves New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
13
books
cite this book:
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- The Fermat Proof by C. J. Mozzochi in Back Matter
- Heegner Modules and Elliptic Curves (Lecture Notes in Mathematics) by Martin L. Brown in Back Matter
- Arithmetic Geometry (Symposia Mathematica) by Fabrizio Catanese on page 168
- Central Simple Algebras and Galois Cohomology (Cambridge Studies in Advanced Mathematics) by Philippe Gille in Back Matter
- Algebraic K-Groups as Galois Modules (Progress in Mathematics) (v. 206) by Victor P. Snaith in Back Matter
See all 13 books citing this book
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