Motives of isogenous \(K3\) surfaces

DOI10.4171/CMH/465zbMath1445.14008arXiv1705.04063OpenAlexW2976105143MaRDI QIDQ2337228

Daniel Huybrechts

Publication date: 19 November 2019

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.04063

zbMATH Keywords

derived categoriesBrauer groups\(K3\) surfacesmotivesHodge conjecturetwisted \(K3\) surfaces

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Algebraic cycles (14C25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) (Equivariant) Chow groups and rings; motives (14C15)

Related Items (14)

Zero-cycles on Garbagnati surfaces ⋮ A remark on the motive of certain moduli spaces on \(K3\) surfaces ⋮ Twisted derived equivalences and isogenies between \(K3\) surfaces in positive characteristic ⋮ Brilliant families of K3 surfaces: twistor spaces, Brauer groups, and Noether-Lefschetz loci ⋮ Hodge similarities, algebraic classes, and Kuga-Satake varieties ⋮ Sixfolds of generalized Kummer type and K3 surfaces ⋮ Motivic cohomology and \(K\)-theory of some surfaces over finite fields ⋮ Algebraic cycles and Verra fourfolds ⋮ A motivic global Torelli theorem for isogenous \(K3\) surfaces ⋮ Motives of moduli spaces on \(K3\) surfaces and of special cubic fourfolds ⋮ Derived categories of surfaces, O’Grady’s filtration, and zero-cycles on holomorphic symplectic varieties ⋮ On certain isogenies between K3 surfaces ⋮ Recognizing Galois representations of K3 surfaces ⋮ CM liftings of surfaces over finite fields and their applications to the Tate conjecture

Cites Work

• Twisted Fourier-Mukai functors
• The Hodge conjecture for self-products of certain \(K3\) surfaces
• Motives of derived equivalent \(K3\) surfaces
• Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics
• Some remarks on L-equivalence of algebraic varieties
• Every rational Hodge isometry between two K3 surfaces is algebraic
• Equivalences of twisted K3 surfaces
• Derived categories of coherent sheaves and motives of K3 surfaces
• Lectures on K3 Surfaces
• ON CORRESPONDENCES BETWEEN K3 SURFACES
• The class of the affine line is a zero divisor in the Grothendieck ring: Via 𝐺₂-Grassmannians
• GENERALIZED CALABI–YAU STRUCTURES, K3 SURFACES, AND B-FIELDS
• Cremona transformations and derived equivalences of K3 surfaces
• Hodge groups of K3 surfaces.
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