
Introduction  Table of Contents  Index  Supplementary Material 
University Lecture Series 2013; 149 pp; softcover Volume: 61 ISBN10: 082189434X ISBN13: 9780821894347 List Price: US$44 Member Price: US$35.20 Order Code: ULECT/61 See also: Mixed Motives  Marc Levine Introduction to Hodge Theory  Jose Bertin, JeanPierre Demailly, Luc Illusie and Chris Peters  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 ChowKünneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of BlochBeilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives. Readership Graduate students and research mathematicians interested in algebraic cycles and motives. 


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