Murre, J. P. Algebraic cycles on abelian varieties: Application of abstract Fourier theory. (English) Zbl 0991.14006 Gordon, B. Brent (ed.) et al., The arithmetic and geometry of algebraic cycles. Proceedings of the NATO Advanced Study Institute, Banff, Canada, June 7-19, 1998. Vol. 1. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 548, 307-320 (2000). From the preface to the whole volume: In this extended lecture notes, the author introduces us to the theory of algebraic cycles on abelian varieties from yet an other viewpoint than his predecessor [see S. Müller-Stach, ibid. 285-305 (2000; see the preceding review Zbl 0991.14005)] over algebraically closed fields. Both results are proved by using the theory of Fourier transforms, in particular the author presents the so-called main theorem of Fourier theory on abelian varieties. This, in turn, can be proved by using the Grothendieck Riemann-Roch theorem. Altogether, this contribution provides deep insights into the structure of Chow groups of abelian varieties and serves as an ideal model for arbitrary varieties.For the entire collection see [Zbl 0933.00032]. Cited in 4 Documents MSC: 14C25 Algebraic cycles 14K05 Algebraic theory of abelian varieties 14F42 Motivic cohomology; motivic homotopy theory 14C40 Riemann-Roch theorems 14C15 (Equivariant) Chow groups and rings; motives Keywords:Fourier theory on abelian varieties; Grothendieck Riemann-Roch theorem; Chow groups of abelian varieties Citations:Zbl 0991.14005 PDFBibTeX XMLCite \textit{J. P. Murre}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 548, 307--320 (2000; Zbl 0991.14006)