On the Tate and Mumford-Tate conjectures in codimension 1 for varieties with \(h^{2,0}=1\)

DOI10.1215/00127094-3774386zbMath1372.14008arXiv1504.05406OpenAlexW3099320216WikidataQ123360398 ScholiaQ123360398MaRDI QIDQ523411

B. J. J. Moonen

Publication date: 20 April 2017

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

Full work available at URL: https://arxiv.org/abs/1504.05406

zbMATH Keywords

\(K3\) surfacecomplex multiplicationKuga-Satake constructionHodge structureMumford-Tate conjectureTate conjecturemotivenorm functor

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Variation of Hodge structures (algebro-geometric aspects) (14D07) Complex multiplication and abelian varieties (14K22) Moduli, classification: analytic theory; relations with modular forms (14J15) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Special surfaces (14J25) (Equivariant) Chow groups and rings; motives (14C15)

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Transcendental Hodge algebra ⋮ Galois representations on the cohomology of hyper-Kähler varieties ⋮ On the Mumford-Tate conjecture for hyperkähler varieties ⋮ Recent progress on the Tate conjecture ⋮ Families of motives and the Mumford-Tate conjecture ⋮ Algebraic geometry: moduli spaces, birational geometry and derived aspects. Abstracts from the workshop held July 10--16, 2022 ⋮ INTEGRAL AND ADELIC ASPECTS OF THE MUMFORD–TATE CONJECTURE ⋮ Explicit families of \(K3\) surfaces having real multiplication ⋮ Variations on a Theorem of Tate ⋮ On the cohomology of surfaces with $p_g = q = 2$ and maximal Albanese dimension ⋮ On compatibility of the \(\ell\)-adic realisations of an abelian motive ⋮ Effective cycles on the symmetric product of a curve, I: the diagonal cone ⋮ \(p\)-adic Tate conjectures and abeloid varieties ⋮ On the motive of O’Grady’s ten-dimensional hyper-Kähler varieties

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