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p-adic Hodge theory and Chow groups of Calabi-Yau 3-folds

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

In a series of two papers, Claire Voisin showed using Hodge theory that if X is a nonrigid Calabi-Yau 3-fold over the complex numbers, then for a general deformation of X, the Griffiths group of codimension two cycles module algebraic equivalence is not finitely generated.  This extends classic results of Griffiths and Clemens.   Let now F be an algebraic closure of a finite field of characteristic p and W(F) its ring of Witt vectors, which is the complete discrete valuation ring of mixed characteristic (p,0) with residue field F in which p is unramified.  We examine a p-adic analogue where X is a lifting of an ordinary Calabi-Yau 3-fold over F to W(F) using the deformation theory of ordinary Calabi-Yau 3-folds that was developed in the thesis of Matthew Ward.  We use p-adic Hodge theory as originally developed in the ordinary reduction case by Bloch-Kato and others.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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