

Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
April 8, 2014 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)






Infinitesimal Hodge conjecture
S. J. Bloch^{} 
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Abstract:
(Joint with H. Esnault and M. Kerz) It is difficult to talk about
infinitesimal deformations of algebraic cycles, but the work of Thomason on
the Ktheory of singular schemes makes it possible, essentially by defining
cycle classes via the chern character applied to vector bundles. Using this
approach, we show that the cohomology class of an algebraic cycle remains
algebraic under infinitesimal deformation if and only if it remains Hodge.
A similar result is proven in mixed characteristic using crystalline cycle
classes.
Language: English

