The Hodge conjecture for Fermat varieties

DOI10.1007/BF01428804zbMath0403.14007WikidataQ123290370 ScholiaQ123290370MaRDI QIDQ1256016

Tetsuji Shioda

Publication date: 1979

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163317

zbMATH Keywords

Hodge ConjectureTate ConjectureAlgebraic CyclesFermat Varieties

Mathematics Subject Classification ID

Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Special surfaces (14J25)

Related Items (39)

On the Picard number of a complex projective variety ⋮ A note on the formal groups of weighted Delsarte threefolds ⋮ Unnamed Item ⋮ On Voisin's conjecture for zero-cycles on hyperkaehler varieties ⋮ Cohomology and the Brauer groups of diagonal surfaces ⋮ Mixed Hodge structure of affine hypersurfaces ⋮ Picard Ranks of K3 Surfaces of BHK Type ⋮ Some desultory remarks concerning algebraic cycles and Calabi-Yau threefolds ⋮ Arithmetic Torelli maps for cubic surfaces and threefolds ⋮ Hodge theory on some invariant threefolds of even degree ⋮ Some results on a conjecture of Voisin for surfaces of geometric genus one ⋮ A remark on the motive of the Fano variety of lines of a cubic ⋮ Diagonal hypersurfaces and the Bloch-Kato conjecture, I ⋮ On cubic fourfolds with an inductive structure ⋮ Algebraic cycles on Fano varieties of some cubics ⋮ Some cubics with finite-dimensional motive ⋮ Tate conjecture for products of Fermat varieties over finite fields ⋮ Some elementary examples of quartics with finite-dimensional motive ⋮ Families of motives and the Mumford-Tate conjecture ⋮ The Hodge conjecture and the Tate conjecture for Fermat varieties ⋮ A note on varieties of weak CM-type ⋮ SOME NEW EXAMPLES OF SMASH-NILPOTENT ALGEBRAIC CYCLES ⋮ A family of cubic fourfolds with finite-dimensional motive ⋮ Algebraic cycles on certain hyperkähler fourfolds with an order 3 non-symplectic automorphism II ⋮ A simple formula for the Picard number of \(K3\) surfaces of BHK type ⋮ Standard conjectures for abelian fourfolds ⋮ Unnamed Item ⋮ Some surfaces with maximal Picard number ⋮ Fermat motives and the Artin-Tate formula. II ⋮ Lines on the Fermat Quintic Threefold and the Infinitesimal Generalized Hodge Conjecture ⋮ Integral Hodge conjecture for Fermat varieties ⋮ The Picard number of certain algebraic surfaces ⋮ Unnamed Item ⋮ The Hodge conjecture for the Jacobian varieties of generalized Catalan curves ⋮ \(G_4\) flux, algebraic cycles and complex structure moduli stabilization ⋮ REFINED MOTIVIC DIMENSION OF SOME FERMAT VARIETIES ⋮ Voisin's conjecture for zero-cycles on Calabi-Yau varieties and their mirrors ⋮ Algebraic cycles and very special cubic fourfolds ⋮ Hodge theory on cyclotomic threefolds (with a view towards the higher dimensional case)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Fermat varieties
• The Hodge conjecture and the Tate conjecture for Fermat varieties
• Hodge's general conjecture is false for trivial reasons
• On some results on the Picard numbers of certain algebraic surfaces
• On the intersection matrix of a hypersurface
• Some Recent Developments in the Theory of Algebraic Varieties

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