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  3. Algebraic Cycles and Motives
    Volume 1
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  • Publisher:
    Cambridge University Press
    Publication date:
    May 2010
    May 2007
    ISBN:
    9780511721496
    9780521701747
    DOI:
    https://doi.org/10.1017/CBO9780511721496
    Dimensions:
    Weight & Pages:
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.514kg, 308 Pages
    • Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (343)
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (343)
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    Book description

    Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This 2007 book is one of two volumes that provide a self-contained account of the subject. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.

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