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ISBN: 3540054995 0387054995 3540368574 Year: 1971 Publisher: Berlin Springer
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Algebraic geometry --- 512 --- Algebra --- Fundamental groups (Mathematics) --- Geometry, Algebraic. --- Schemes (Algebraic geometry) --- Topological groups. --- 512 Algebra --- Fundamental groups (Mathematics). --- Schemes (Algebraic geometry). --- Géométrie algébrique
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ISBN: 082189434X 9780821894347 Year: 2013 Publisher: Providence American Mathematical Society
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The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to have a number of additional properties predicted by Grothendieck's standard conjectures, but these conjectures remain wide open. The theory for mixed motives is still incomplete. This book deals primarily with the theory of pure motives. The exposition begins with the fundamentals: Grothendieck's construction of the category of pure motives and examples. Next, the standard conjectures and the famous theorem of Jannsen on the category of the numerical motives are discussed. Following this, the important theory of finite dimensionality is covered. The concept of Chow-Künneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of Bloch-Beilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives -- P. 4 of cover.
ISBN: 354058692X 3540490469 9783540586920 Year: 1994 Volume: 1594 Publisher: Berlin Springer
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Algebraic geometry --- Algebraic cycles --- Hodge theory --- Congresses --- 512.73 --- Complex manifolds --- Differentiable manifolds --- Geometry, Algebraic --- Homology theory --- Cycles, Algebraic --- Congresses. --- Cohomology theory of algebraic varieties and schemes --- 512.73 Cohomology theory of algebraic varieties and schemes --- Algebraic cycles - Congresses. --- Hodge theory - Congresses. --- Algebraic cycles - Congresses --- Hodge theory - Congresses
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