CM liftings of surfaces over finite fields and their applications to the Tate conjecture

DOI10.1017/fms.2021.24zbMath1477.14042arXiv1809.09604OpenAlexW3155444469WikidataQ123154602 ScholiaQ123154602MaRDI QIDQ4988393

Kazuhiro Ito, Teruhisa Koshikawa, Tetsushi Ito

Publication date: 14 May 2021

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.09604

zbMATH Keywords

\(K3\) surfacesTate conjectureCM lifting

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items

Construction of quasi-canonical liftings of \(K3\) surfaces of finite height in odd characteristic ⋮ On irreducible symplectic varieties of \(\operatorname{K3}^{[n}\)-type in positive characteristic] ⋮ ERRATUM TO APPENDIX TO ‘2-ADIC INTEGRAL CANONICAL MODELS’ ⋮ Logarithmic Riemann–Hilbert correspondences for rigid varieties

Cites Work

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• Orders of automorphisms of \(K3\) surfaces
• The Tate conjecture for \(K3\) surfaces over finite fields
• Supersingular \(K3\) surfaces for large primes. With an Appendix by Andrew Snowden.
• Relations between Dieudonné displays and crystalline Dieudonné theory
• The Tate conjecture for \(K3\) surfaces in odd characteristic
• Frames and finite group schemes over complete regular local rings
• \(K3\) surfaces over finite fields with given \(L\)-function
• The Tate conjecture for ordinary K 3 surfaces over finite fields
• \(K3\) surfaces of finite height over finite fields
• Théorie de Dieudonne cristalline. II
• F-isocrystals and De Rham cohomology. I
• Tate's conjecture for \(K3\) surfaces of finite height
• \(p\)-adic étale cohomology
• Cycle classes and Riemann-Roch for crystalline cohomology
• \(p\)-adic étale cohomology and crystalline cohomology in the semi-stable reduction case
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• On the generic part of the cohomology of compact unitary Shimura varieties
• Integral \(p\)-adic Hodge theory
• On the Shafarevich and Tate conjectures for hyperkähler varieties
• Construction of semi-stable \(p\)-adic representations
• Every rational Hodge isometry between two K3 surfaces is algebraic
• Motives of isogenous \(K3\) surfaces
• The correspondence between Barsotti-Tate groups and Kisin modules when \(p=2\)
• Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux. Exposés VIII à XVIII. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3) dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Théorie de Hodge. II. (Hodge theory. II)
• Lectures on Supersingular K3 Surfaces and the Crystalline Torelli Theorem
• -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES
• Lattices in Filtered (φ, N)-modules
• K3 surfaces with algebraic period ratios have complex multiplication
• -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES – CORRIGENDUM
• 2-ADIC INTEGRAL CANONICAL MODELS
• Mod $p$ points on Shimura varieties of abelian type
• Generic base change, Artin’s comparison theorem, and the decomposition theorem for complex Artin stacks
• Kuga-Satake abelian varieties of K3 surfaces in mixed characteristic
• Integral models for Shimura varieties of abelian type
• Nagata compactification for algebraic spaces
• Non-archimedean analytification of algebraic spaces
• Néron Models
• ELLIPTIC MODULES
• Clifford Algebras and Spinor Norms Over a Commutative Ring
• Formal groups arising from algebraic varieties
• Integral crystalline cohomology over very ramified valuation rings
• Breuil–Kisin modules via crystalline cohomology
• Hodge groups of K3 surfaces.
• DISPLAYED EQUATIONS FOR GALOIS REPRESENTATIONS
• The -cohomology in the semistable case
• ERRATUM TO APPENDIX TO ‘2-ADIC INTEGRAL CANONICAL MODELS’
• Berkeley Lectures on p-adic Geometry
• A Néron–Ogg–Shafarevich criterion for K3 surfaces
• Recent progress on the Tate conjecture
• Integral canonical models for Spin Shimura varieties
• La filtration canonique des points de torsion des groupes $p$-divisibles
• Perfectoid Spaces: A survey
• Mixed Hodge Structures
• Crystalline representations and F-crystals
• Algèbre