\(p\)-adic deformation of algebraic cycle classes

DOI10.1007/s00222-013-0461-4zbMath1301.19005arXiv1203.2776OpenAlexW1983055236MaRDI QIDQ2449837

Hélène Esnault, Moritz Kerz, Spencer Bloch

Publication date: 12 May 2014

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.2776

zbMATH Keywords

de Rham cohomologyHodge filtrationalgebraic cyclesMilnor \(K\)-theoryde Rham-Witt complexfundamental triangle\(p\)-adic deformationcrystalline Chern charactercrystalline Hodge obstructionFontaine-Messing-Kato syntomic complexFontaine-Messing's \(p\)-adic variational Hodge conjectureGrothendieck's variational Hodge conjecturemotivic pro-complexSuslin-Voevodsky motivic complextopological cyclic homological theory

Mathematics Subject Classification ID

Variation of Hodge structures (algebro-geometric aspects) (14D07) de Rham cohomology and algebraic geometry (14F40) Algebraic cycles (14C25) (p)-adic cohomology, crystalline cohomology (14F30) Formal methods and deformations in algebraic geometry (14D15) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15)

Related Items (13)

Chern character and obstructions to deforming cycles ⋮ Towards connectivity for codimension 2 cycles: infinitesimal deformations ⋮ Non-liftability of automorphism groups of a \(K3\) surface in positive characteristic ⋮ Algebraic geometry in mixed characteristic ⋮ Continuous \(K\)-theory and cohomology of rigid spaces ⋮ Syntomic complexes and \(p\)-adic nearby cycles ⋮ \(p\)-adic deformation of motivic Chow groups ⋮ A variational Tate conjecture in crystalline cohomology ⋮ Étale cohomology of arithmetic schemes and zeta values of arithmetic surfaces ⋮ Weil-étale cohomology and zeta-values of proper regular arithmetic schemes ⋮ \(p\)-adic Tate conjectures and abeloid varieties ⋮ 𝐾-theory and topological cyclic homology of henselian pairs ⋮ On the Beilinson fiber square

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