Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for \(K3\) surfaces, and the Tate conjecture

DOI10.4007/annals.2016.184.2.4zbMath1387.14102arXiv1407.0592OpenAlexW2963947728WikidataQ123367060 ScholiaQ123367060MaRDI QIDQ350552

François Charles

Publication date: 7 December 2016

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0592

zbMATH Keywords

\(K3\) surfacesholomorphic sympltic varietiesTate conjecture

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Parametrization (Chow and Hilbert schemes) (14C05) Finite ground fields in algebraic geometry (14G15)

Related Items (18)

Galois representations on the cohomology of hyper-Kähler varieties ⋮ Homotopic and geometric Galois theory. Abstracts from the workshop held March 7--13, 2021 (online meeting) ⋮ Finiteness of Lagrangian fibrations with fixed invariants ⋮ Singularities of normal quartic surfaces. I: (\(\mathrm{char}= 2\)) ⋮ A global Torelli theorem for singular symplectic varieties ⋮ Non-Abelian Lefschetz hyperplane theorems ⋮ Erratum to: ``The Tate conjecture for \(K3\) surfaces over finite fields ⋮ Recent progress on the Tate conjecture ⋮ Algebraic geometry: moduli spaces, birational geometry and derived aspects. Abstracts from the workshop held July 10--16, 2022 ⋮ The K3 category of a cubic fourfold ⋮ On irreducible symplectic varieties of \(\operatorname{K3}^{[n}\)-type in positive characteristic] ⋮ Derived equivalences of twisted supersingular \(K3\) surfaces ⋮ Arithmetic of K3 Surfaces ⋮ Pathologies of the Hilbert scheme of points of a supersingular Enriques surface ⋮ Finiteness theorems for K3 surfaces and abelian varieties of CM type ⋮ Moduli spaces of sheaves on \(K3\) surfaces and Galois representations ⋮ Rational points and derived equivalence ⋮ Reduction of Brauer classes on K3 surfaces, rationality and derived equivalence

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