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Transcendental numbers --- Motives (Mathematics) --- Algebraic fields

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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.

Algebraic cycles --- Motives (Mathematics) --- Theory of motives (Mathematics) --- Algebraic varieties --- Homology theory --- Cycles, Algebraic --- Geometry, Algebraic

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Presents the research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods.

Feynman integrals. --- Motives (Mathematics) --- Quantum field theory. --- Algebra --- Feynman integrals --- Quantum field theory