The Hodge conjecture and the Tate conjecture for Fermat varieties

DOI10.3792/pjaa.55.111zbMath0444.14017OpenAlexW2045787135WikidataQ123262821 ScholiaQ123262821MaRDI QIDQ1144621

Tetsuji Shioda

Publication date: 1979

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.55.111

zbMATH Keywords

Hodge conjecturecharacteristic pTate conjectureFermat variety

Mathematics Subject Classification ID

Arithmetic ground fields for abelian varieties (14K15) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Special surfaces (14J25) Arithmetic problems in algebraic geometry; Diophantine geometry (14G99)

Related Items (9)

On certain arithmetical invariants of Fermat varieties ⋮ The Tate conjecture for powers of ordinary cubic fourfolds over finite fields ⋮ Small codimension components of the Hodge locus containing the Fermat variety ⋮ Tate conjecture for products of Fermat varieties over finite fields ⋮ A category of kernels for equivariant factorizations and its implications for Hodge theory ⋮ Fermat motives and the Artin-Tate formula. II ⋮ The Hodge conjecture for Fermat varieties ⋮ Algebraic cycles on Abelian varieties of Fermat type ⋮ Transcendental cycles on ordinary K3 surfaces over finite fields

Cites Work

• On Fermat varieties
• The Hodge conjecture for Fermat varieties
• Endomorphisms of Abelian varieties over finite fields
• Numbers of solutions of equations in finite fields
• Jacobi Sums as "Grossencharaktere"
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