Algebraic cycles of abelian varieties

DOI10.1215/S0012-7094-83-05021-4zbMath0521.14002OpenAlexW4241790079MaRDI QIDQ1055497

V. Kumar Murty

Publication date: 1983

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-83-05021-4

zbMATH Keywords

Picard numberHodge conjectureHodge ring of Abelian varietypole of L-seriesTate conjecture on cycles

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Zeta functions and (L)-functions of number fields (11R42) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Related Items

The Hodge Group of an Abelian Variety, Families of motives and the Mumford-Tate conjecture, Tate cycles on a product of two Hilbert modular surfaces, An overview of the mathematical work of Fumiyuki Momose, Algebraic cycles on compact Shimura surface, Exceptional Hodge classes on certain abelian varieties, Overview of the Work of Kumar Murty

Cites Work

• Twists of modular forms and endomorphisms of abelian varieties
• Newforms and functional equations
• A note of Shimura's paper: Discontinuous groups and Abelian varieties
• Algebraic cycles on abelian varieties of complex multiplication type
• On a convolution of L-series
• On automorphic forms on \(mathrm{GL}_2\) and Hecke operators
• Class fields over real quadratic fields and Hecke operators
• The special values of the zeta functions associated with cusp forms
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
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